Are there ever any interactions between Lord Shiva and Goddess Lakshmi (as in a brother-sister relationship, obviously)?

 Yes according to karveer mahatmya and local kolhapur traditions and folks, king jyotība (an incarnation of shankara) shares siblings relation to Ambabaī (an incarnation of laksmī ).

Jyotība an incarnation of shankara who shares sibling bond with ambabaī, and who is king of dakkhan (an sacred place in maharashtra) and who defeated asuras like ratnasur and raktabhoj.

Ambabaī, lately know as Mahalakshmī incarnation of laxmī who shares sibling relation with jyotība, she is ruler of karveera lately known as kolhapur (an very sacred place in maharashtra) and she struck terror and slayed an demon named kolhasura.

[According to karveer mahatmya, padma purana, maharashtra/kolhapura tradition & local folks]

Nextly according to atharvana rahasya of laxmihrudayamstotram.

Lakshmī is as same tattva swaroopa as sadashīva.

Shīva is also same tattva swaroopa as laxmī.

And as an advaīt vedanta, i worship them as eternal siblings.

|| Shrī matarayé namaha ||

How did Lord Vishnu get Goddess Lakshmi as his consort?

 In Hinduism, you will often find multiple narratives that vary or even appear to contradict one another. This is due to Kalpa Bheda, varying Sampradayas, or Kula lineages. Ultimately, the Supreme Truth is experienced and described from different perspectives.

According to texts like the Srimad Devi Bhagavatam, the Devi Mahatmya, and Lakshmi Tantra, it is Mahadevi who manifests and assigns consorts to the Tridevas (Brahma, Vishnu, and Shiva). Similarly, texts like the Varaha Mahapurana and Padma Purana state that when the Supreme Purusha manifests as the Tridevas, Para-Prakriti simultaneously manifests as the Tridevi.

However, a highly specific and fascinating account is found in the Sri Dakshinamurti Samhita, which states that Sri Hari Vishnu practiced Vaishnavi Vidya to obtain Goddess Lakshmi as his wife.

Sri Dakshinamurti Samhita, Chapter Four:

Translation: "Now, O Great Goddess, I shall describe the deity of supreme empire, by whose worship Vishnu himself became the Lord of Lakshmi (Lakshmipati)."

The Form of the Goddess

The presiding deity of this Vidya is none other than Sarva-Samrajya-Lakshmi. The text provides a Dhyana on her divine form, which Lord Vishnu utilized during his worship:

Translation: "She resembles the Atasi flower (blue flax) and is adorned with gem-studded ornaments. In six of her hands, she holds the Conch (Shanka), Discus (Chakra), Mace (Gada), Lotus (Padma), Bow (Sharnga), and Arrows (Bana). With two other hands, she displays the gestures of Boon-giving (Varada) and Fearlessness (Abhaya). Meditating thus on her eight-armed form, the wise one should perform the recitation."

This is consistent with other sources, which note that Lord Vishnu successfully undertook the Sadhana of Goddess Kamala to gain her as his eternal consort.

Kamalā Kamalā 🌺🪷

Maa Sarva Samrajya Lakshmi.