Perhaps too esoterick for most of my readers, but here is a ChatGPT analysis of the (syncretist) relation between Tripura Sundari and Lakshmi. Somewhat edited.
[...]
This is a particularly interesting passage because it provides a scriptural explanation for the relationship between Tripura Sundari, Mahalakshmi, and Sri Vidya. And, importantly, it is more nuanced than simply identifying two goddesses with one another.
The account is indeed discussed by Rajmani Tigunait in Śakti: The Power in Tantra. I was able to locate the relevant passage in Chapter 2, together with his scholarly qualification immediately following it.
The story of Lakshmi's meditation
According to the Tripura Rahasya, Māhātmyakhaṇḍa 53:42–47, Lakshmi (here called Sri) undertakes an extraordinarily long period of meditation upon Tripura Sundari.
When Tripura finally appears and offers her a boon, Lakshmi requests sāyujya-mukti: liberation through union with the Goddess, essentially becoming one with her.
Tripura, however, points out that Vishnu needs Lakshmi in order to fulfil his role as protector and preserver of the universe. If Lakshmi were to merge completely with Tripura, Vishnu would be unable to perform that function.
Instead, Tripura grants her a different, remarkable boon.
The relevant Sanskrit passage, as reproduced in Tigunait's notes, reads:
Śrīvidyety aham ākhyātā śrīpuraṃ me puraṃ bhavet
Śrīcakraṃ me bhavec cakraṃ śrīkramaḥ syān mama kramaḥ
Śrīsūktam etad bhūyān me vidyā śrīṣoḍaśī bhavet
Mahālakṣmīty ahaṃ khyātā tvattādātmyena saṃsthitā
In substance, Tripura declares:
I shall be known as Sri Vidya.
Sri-pura shall be my divine city.
Sri Chakra shall be my sacred diagram.
Sri's ritual order shall become my ritual order.
The Sri Sukta shall become associated with my sixteen-syllabled Vidya.
Through my essential identity with you, I shall be known as Mahalakshmi.
This is a fascinating theological arrangement: rather than Lakshmi abandoning her cosmic responsibilities to merge with Tripura, Tripura incorporates Lakshmi's identity, name and sacred symbolism into her own worship.
What does this mean theologically?
I think there are three possible levels of interpretation.
A. Tripura Sundari as the supreme Goddess
In this interpretation, Tripura is the ultimate divine reality, and Lakshmi is one of the ways that reality manifests.
Lakshmi's desire for union is therefore not necessarily a relationship between two entirely separate deities. It can be understood as a manifestation of Shakti seeking complete union with the supreme Shakti.
This is consistent with the broader Sri Vidya understanding of Tripura as the supreme consciousness and power underlying the universe.
B. Lakshmi as an independent goddess who shares Tripura's essential nature
This is perhaps the most interesting interpretation of the actual story.
Lakshmi is not portrayed as an inferior deity or merely an attendant of Tripura. She has her own identity and her own cosmic responsibility alongside Vishnu.
Tripura does not simply absorb her. Instead, she establishes an enduring identity between them while allowing Lakshmi to continue her divine function.
The expression tvattādātmyena saṃsthitā is particularly important: it conveys the idea of being established in essential identity with you.
C. Sri Vidya as a tradition incorporating Lakshmi
This is where the historical interpretation becomes important.
Tigunait points out that the story may explain how Lakshmi's name, symbolism and worship became integrated into the Tripura Sundari tradition.
He explicitly cautions against concluding that Tripura Sundari is simply a form of Lakshmi, or that Lakshmi is simply a form of Tripura Sundari.
In other words, the text establishes a theological unity, but that does not automatically establish universal interchangeability across Hindu traditions.
An interesting connection: the Sri Sukta
One detail in the passage deserves particular attention.
Tripura says that the Sri Sukta will become associated with her own sixteen-syllabled Vidya.
The Sri Sukta is one of the oldest and most important Vedic hymns to Sri/Lakshmi. It praises her as the source of prosperity, beauty, fertility, splendour and auspiciousness.
This means that the story is doing something quite substantial: it connects an ancient Vedic tradition of Lakshmi worship with the later Tantric tradition of Tripura Sundari.
It also helps explain why the word Sri is so prominent in Sri Vidya.
There is another interesting detail: Tigunait discusses the traditional interpretation of the final syllable of the sixteen-syllabled Tripura mantra, Śrīṃ, as the source of the name Sri Vidya.
Does this mean Lakshmi can be worshipped independently of Vishnu?
I would say that this story provides a particularly strong theological justification for doing so.
Notice that Lakshmi is not required to abandon her identity or her relationship with Vishnu. Tripura explicitly acknowledges Vishnu's dependence upon her.
But Lakshmi's spiritual aspiration is directed towards Tripura Sundari.
This suggests that Lakshmi has a devotional and spiritual dimension that is not exhausted by her role as Vishnu's consort.
My overall interpretation: The most important implication of this story is that Lakshmi and Tripura Sundari are presented as sharing an essential divine identity without necessarily losing their distinctive personalities and functions.
That is a rather beautiful theological possibility. It allows one to regard Lakshmi as a fully independent object of devotion while simultaneously understanding her as an expression of the supreme Shakti represented by Tripura Sundari.
For further reading, the most relevant sources are:
Rajmani Tigunait, Śakti: The Power in Tantra, Chapter 2, especially pp. 35–36 and note 51.
Tripura Rahasya, Māhātmyakhaṇḍa 53:42–47.
You can also consult the Tripura Rahasya translation.