Is Lalita Tripurasundari an inferior amsha of Radha?

 See, being a Maadhva, my answer can differ from other people. Since you have requested this answer, I will answer it. Please forgive me if I go wrong anywhere. Umm…if you see, then Lalita Tripurasundari is different and Radha is different. I have heard that Lalita Tripurasundari as per Shaktas is one of the 10 Mahavidyas known as Sri Shodashi devi. One must note that SriLalita Tripurasundari is different from SriLalita sakhi of Srimati Radharaniji. This answer will be based on Vaishnava perspective, especially Madhva siddhanta. I don’t know much about Shaktism so I won’t talk from that lens, plus I am not even a Shaakta.

HOW MIGHT SRILALITA TRIPURASUNDARI BE UNDERSTOOD FROM A MADHVA PERSPECTIVE?

From the Madhva perspective, the answer would be no. We do not place Srimati Radharaniji in a position from which Lalita Tripurasundari would be considered her amsha. SriMadhvacharya mentions that Lord Narayana is the supreme. Plus, Mahalakshmi devi is the second one after SriNarayana. And Lakshmi has three forms namely : Sri, Bhu and Durga via which She is the presiding deity for Satva (Sri), Rajas(Bhu) and Tamas(Durga) Guna. All the roopas are identical with Mahalakshmi devi and are non-different from them. Now, here too there are two cases based on what one believes:

1. SriLalita Tripurasundari is Durga Parameshwari:

If you consider Her as Durgadevi then in this case, She may be understood as Durga devi who is the form of Mahalakshmi devi. Because, in Lakshmi Tantra, Lakshmidevi says :

bhadrakALI tathA bhadrA kALI durgA maheSvarI |
triguNA bhagavatpatnI tathA bhagavatI parA ||

Further, the people address Me as BhadrakALi, BhadrA, kALi, Durga, Maheshvari, triguna and by other names. They also call Me as Bhagavati since I am the consort of Bhagavan.

mahattvAcca mahAmAyA mohanAnmohinI matA |
durgA ca durgamatvena bhaktarakshAvidherapi ||

I am worshipped as MahAmAyA since My mAya/mahatvam (greatness) pervades everywhere. I am saluted as Mohini since I immerse all in moham (delusion). I am called Durga because I am hard to attain and also because I protect My bhaktAs.

अहं श्रीश्च महीं चैव दुर्गां चैव सनातनम् ।
बिभर्मी त्रिभिरूपैस्तु जगदेतच्चराचरम् ॥
I am indeed Śrī, I am Mahī (Bhū/Earth), and I am the eternal Durgā. Assuming these three distinct forms, I sustain and carry this entire universe of moving and unmoving beings.

[Lakshmi Tantra, Pancharaatra aagama]

So, as per this, SriLalita Tripurasundari may be understood as Durga roopi Mahalakshmi’s form. Because, Durgadevi is Vishnumaya Durga, even as per Devi Mahatmya. Lakshmi devi can do creation, sustainance and destruction just by Her eyebrow movement. And all this is possible due to Lord Narayana’s grace.

2. SriLalita Tripura Sundari as Parvatidevi’s roopa:

Like Lakshmi devi has Durga roopa, Umadevi also has a Durga roopa. This form is what we call as Kaushiki or Mahasarasvati. In this form She killed Shumbha and Nishumbha named demons. So, if you believe SriLalita Tripurasundari as Parvati devi’s Durga roopa then, She has the sannidhana of Vishnumaya roopi Mahalakshmi, similar to how Mahasarasvati had.

When the devatas were frustrated by the nuisance caused by Shumbha and Nishumbha, they approached Kailasa and prayed to Vishnumaya Durga. At that time, Parvati devi was going for having a bath where She sees the devatas praying to someone. She asks, ‘Whom are you all praying to?’ At the same time, a devi came out of Her body cell, who was dark skinned, but radiant and held a bell, trident, plough, conch shell, pestle (a cylindrical club), discus, bow and arrows in Her hands. Since, She came from Umadevi’s body cell, She was known as Kaushiki (Kosha means cell). She said, ‘They all are worshipping me.’

[Mahasarasvati roopa : Durga roopa of Umadevi]

Earlier Umadevi had dark skin. Once, Lord Shiva called Her Kaali, due to which She felt insulted and did penance to Lord Brahma and asked for a new body. Lord Brahma blessed Her with a new body, which was of Gaura varna or golden color. Since, She got a golden body, She was known as Gowry/Gauri. Now, this dark body didn’t go in vain. Because, devata body never goes waste. Hence, due to Her shakti, the body remained in Her body. Devatas do have this kind of power. Now, when these devatas were calling for Vishnumaya Durga, this Vishnumaya Durga entered that dark skinned body within Parvati’s body. That body had some sannidhana of Umadevi. So, this roopa is Parvati’s Durga roopa known as Mahasaraswati or Kaushiki or Chandika Durga.

So, in this way SriLalita Tripurasundari too might have the presence of Vishnumaya Durga, if you consider Her as Umadevi’s roopa.

As per Madhva sampradaya if you see, Srimati Radharaniji is not considered as Lakshmi avatara, since SrimadBhagavatam or the Mahabharata too doesn’t mention about Her. Plus, SriMadhvacharya too doesn’t mention about Her neither in the SriMahabharata Tatparya Nirnaya, nor the SriBhagavata Tatparya Nirnaya. But, She can be considered as a Gopi who is favorite of Krishna in Vrindavana with Lakshmidevi’s special sannidhana in Her. Srimati Radharaniji is a great devotee of Krishna in Vrindavana, but we don’t consider Her as equal to Mahalakshmidevi, because the Gopikas are the incarnation of Apsaraa strees who had came on the earth to get the sanga of Krishna. Apsaraas have their niyata pati as Lord Narayana, and they worship Lord Narayana as their husband. So, whenever they have Lakshmi sannidhana, Lord Narayana accepts them.

So, we don’t consider Lalita Tripurasundari as an inferior amsha of Srimati Radharaniji, but we don’t either consider Lalita Tripurasundari as the supreme mother ruling the trinity. The above two cases may hold true (Case 1 : Lalita Tripurasundari as Durga Parameshvari and Case 2 : Lalita Tripurasundari as Umadevi’s one form) only iff you believe in it and as per your belief. I am not claiming any certainty because it is completely conditional as to what you believe.
Hope this helps!
Jay SriRam!
ShriKrishnarpanamastu!

To which goddess does Sri Chakra belong? Is it Sridevi Mahalakshmi (Vishnupatni) or Lalita Tripurasundari (Shivpatni)?

 The Adhiṣṭhātrī Devī of Śrī Cakra is Devī Mahālakşmi. She is Kāmeśvara Maheśvarī, Supreme Consort of Kāmeśvara Śiva. She is the empress of Maṇidvīpa. She is Mahātripurā Sundarī Lalitā.

The Brahmāṇḍa Mahāpurāṇa, which sings the glory of Parāśakti Lalitā, clearly states that Śrī Cakra is her Yantra.

मन्त्रं श्रीचक्रगेवास्याः सेयं हि त्रिपुरांबिका ।
सैषैव हि महालक्ष्मीः स्फुरच्चैवात्मनः पुरा ॥ ३ ॥

3. Śrī Cakra alone is her Mantra (Yantra). She is Tripurāmbikā and she is Mahālakṣmī herself. Formerly, the Cakra was seen coming out of Ātman throbbing and sparkling.

~ Brahmāṇḍa Mahāpurāṇa, Upasaṃhārapāda, Lalitopākhyāna, Chapter 41

त्रिमूर्तिजननीमंबां दृष्ट्वा श्रीचक्ररूपिणीम् ।

119. She who is the mother of the Trimūrtis (Brahmā, Viṣṇu and Śiva) and who is present there in the form of Śrīcakra.

~ Brahmāṇḍa Mahāpurāṇa, Upasaṃhārapāda, Lalitopākhyāna, Chapter 40

कामाक्ष्यैव महालक्ष्मीश्चक्रं श्रीचक्रमेव हि।

15. Kāmākşi alone is Mahālakşmi. The Cakra is Śricakra itself.

~ Brahmāṇḍa Mahāpurāṇa, Upasaṃhāra-pāda, Lalitopākhyāna, chapter 41

तस्या मन्त्रमिति प्रोक्तं श्रीचक्रं चक्रूषणम् ।
नवावरणमीशानी श्रीपरस्याधिदैवतम् ॥ ४ ॥

4. Her Mantra also has been mentioned. So also the Śrī Cakra which has nine outer coverings and the mystic circles as its ornaments. (You have mentioned that) Īśānī is the presiding deity of Śrīpura.

~ Brahmāṇḍa Mahāpurāṇa, Upasaṃhārapāda, Lalitopākhyāna, Chapter 39

🪷 Devī Lalitā Tripurā Sundari 🪷 (PC: saitharunvs)

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Bhāvana Upaniṣad depicts the human body as a Śrī Yantrā (Śrī Cakra), associating each body part with a specific Cakra and in the Śrī Cakra, Devī Lalitā is the supreme divinity.

नवशक्तिरूपं श्रीचक्रम् ।

It is the Śrī Cakra in the guise of the nine wheels.

सदानन्दपूर्ण स्वात्मेव परदेवता ललिता ।

The supreme divinity, Lalita, is one’s own blissful Self.

~ Bhāvana Upaniṣad, Atharva Veda

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One of the Śākta Āgamas, the Vāmakeśvara Tantra, thoroughly explains the worship of the Śrī Cakra. It enumerates the nine Āvaraṇas, lists the Devīs in each Āvaraṇa (Āvaraṇa Devatās), the Cakreśvarī of each Āvaraṇa, meditation on the Bindu of the Cakra, and other details concerning the Śrī Cakra, Mudrās, and Śrī Vidyā. And Vāmakeśvara Tantra says at the Bindu resides Śrī Mahābhaṭṭārike Parāpara Rahasya Yoginī Lalitāmbikā and she move within Śrī Cakra.

त्वां गौरीं त्रिपुरां परात्परकलां श्रीचक्रसञ्चारिणीम्

You are Gaurī, Tripurā, the supreme transcendental energy, who moves within the Śrī Cakra.

~ Vāmkeśvara Tantra

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In the Tripurā Rahasya, Devī herself affirms that the Yantra representing her is the Śrī Cakra.

श्रीविद्योत्यहमाख्याता श्रीपुरं मे पुरं भवेत्।
श्री चक्रं मे भवेच्चक्रं श्रीक्रमः स्यान्मममक्रमः॥ ४६॥

46. Henceforth, I will be renowned as "Śrī Vidyā." My city will be famously known as "Śrīpura". The Cakra related to me will be known as "Śrī Cakra", and the Krama associated with me will be known as "Śrī Krama".

~ Tripurā Rahasya, Māhātmya Khaṇḍa, Chapter 53

🪷 Devī Lalitā and Kāmeśvara Śiva surrounded by the Nithyā Devīs 🪷(PC: swaroop_621)

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While commenting on the name “Śrī Cakra Rājanilayā”, Śrī Bhāskararāya Makhin in his Lalitā Sahasranāma Bhāṣya mentions that Śiva and Devī reside in Śrī Cakra.

श्रीचक्रराजं बिन्दुत्रिकोणादिरूपं निलयो वासस्थानं यस्याः। तदुक्तं'श्रीचक्रं शिवयोर्वपु'रिति। शरीरे यथा जीवस्याव स्थानं तथा श्रीचक्रे शिवयोरिति तदर्थः ।

Śrī Cakra, consisting of Bindu, triangle, etc. It is said, "Śrī Cakra is the body of Śiva and Devī." The meaning is just as the Jiva resides in the body so they reside in the Śrī Cakra.

~ Saubhāgya Bhāskara (Commentry on Lalită Sahasranāma) by Bhāskararāya Makhin

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The Stōtras praising Bhagavatī also states that Devī Lalitā is Śrī Cakra Vāsinī.

श्रीचक्रस्थां शाश्वतैश्वर्यदात्रीं पौण्ड्रं चापं पुष्पबाणान् दधानाम् ।
बन्धूकाभां भावयामि त्रिनेत्रां तामग्निवर्णां तपसा ज्वलन्तीम् ॥ ३९ ॥

I bow to that Devī who shines with penance; who resides in Śrī Cakra; who possess inperishable wealth and who bears sugarcane bow and flowry arrows and has three eyes of reddish hue.

~ Śrī Ādi Śaṅkarācārya Viracita Tripurasundarī Vēda Pāda Stotram

श्रीविद्यां शिववामभागनिलयां ह्रीङ्कारमन्त्रोज्ज्वलां श्रीचक्राङ्कितबिन्दुमध्यवसतिं श्रीमत्सभानायिकाम् ।

Devī Mīnākṣi, Who is Śrī Vidhyā shining with the splendour of Hrīṅkāra mantras, where she is residing as the left-half of Śiva,
Within the bindu, at the center of the Śrī Cakra; and presiding over the assembly of deities in the Śrī Cakra.

~ Śrī Ādi Śaṅkarācārya Viracita Mīnākṣi Pañcaratnam

कुण्डल त्रिविधकोण मण्डल विहार षड्दल समुल्लसत्।

Devī Lalitā, Who shines in the six petals, surrounding the triangle in the middle of the (Śrī Cakra)

~ Śrī Ādi Śaṅkarācārya Viracita Navaratna Mālikā

🪷 Śrī Cakra Rāja 🪷 (PC: Google)

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Note: The Cakra or Yantrā of Devī Lakṣmī is the Lakṣmī Yantrā, which is also known as the Śrī Yantrā since another name for Devī Lakṣmī is Śrī. However, this does not make her the Adhiṣṭhātrī Devī of the Śrī Cakra Rāja. Devī Lakṣmī resides in the Lakṣmī Yantrā, and the methods of worshipping her Yantrā, including the Āvaraṇa Devatās, Dhyāna, and Nyāsa, are entirely different. Thus, the Lakṣmī Yantrā and the Śrī Yantrā are distinct from each other.

🪷Śrīmātrē Namaḥ🪷