In some temples and photos, there are images depicting Goddess Lakshmi seated on the thigh of Vigneshwara.
Let us see why is it like that?.
This Goddess Lakshmi is not Vishnu's consort; she is the presiding deity of wealth and prosperity (Aishwarya). Furthermore, the deity depicted is not the standard Vigneshwara we usually envision, but rather Mula Ganapati, Maha Ganapati, or Lakshmi Ganapati.
When Lord Maha Vishnu instructed Sage Vyasa, "The Kali Yuga is approaching, and living beings will face great hardships; organize the Vedas systematically so that they may easily attain salvation and peace of mind," Vyasa set out to classify the Vedas and compose the eighteen Puranas and eighteen Upapuranas. However, he could not make any progress—not even a single sentence or letter would come forth. Astonished and perplexed, he meditated upon Lord Brahma. Upon receiving Brahma's vision and explaining the situation, Brahma said, "Parameshwara had commanded me to begin the work of creation. I did not understand what to do or how to proceed. It was then that I meditated upon Ganapati, and He granted me a vision. He appeared thus:
vakratunda mahAkAya
kOTi sUrya samaprabha “
It was upon beholding Him that my delusion vanished, and I was able to carry out the task of creation without obstacles." Hearing this, Sage Vyasa also meditated upon Ganapati and, through His grace, was able to bestow upon us a magnificent wealth of knowledge.
He is the very same Maha Ganapati, Vallabha Ganapati, or Lakshmi Ganapati.
He is eternal and beginningless (Anadi). He is so ancient that even the celestial wedding of Shiva and Parvati commenced with the worship of Ganapati. On Vinayaka Chavithi, even when various forms of Ganapati—such as Chintamani, Siddhi, Lakshmi, and Pushti—are installed, the initial worship is always offered to "Haridra Ganapati" (the Turmeric Ganapati). He manifests in numerous forms; notably, the Lord bestows His grace through thirty-two distinct forms. There is nothing He cannot grant to His devotees.
The idol is installed in that manner to signify that He is the bestower of prosperity.
Subhamastu