Lalita has got that name as she recides on the ( lalathi + vilasathi ) VAMAANKA of SRI SADA SIVA. She is the adhistana devatha of Panchadasi Stothram and she is the one who bestows mahadaishwaryam to a sadhaka of SRI VIDYA. She is the one who is in the second Avarana of the tripurams so she is known as the Lalitha Tripura Sundari and she is known so as she is exsisting prior to Brahma, Vishnu and Mahesha. On the Sixth day of navarathri Kanakadurga is decorated as LalithatripuraSundari, she is the chaitanya, Echa and Gnyana Shakthi Swaroopini. Even listening to her name is considered to be beneficial to the sadhaka.
Worshiping her is the vital part in the shakti pooja. Kanaka durga is decorated as Bala as SRI ADI SHANKARA, has established srichakra here and so to beget the anugraha of bala she is decorated as bala and one has to def see her beauty in this alankaram. In the first amnaya of srichakra bala resides, so without worshiping bala one cannot perform pooja to sridevi. Without having got the mantra of bala one is not eligible to perform the sri yantra pooja. On the fifth day Kanaka Durga is decorated as Balatripura Sundari, Balatripura is the first goddess in the tripura traya and she is the main goddess of all in the sriyantra. Gayatri is of two types LAghu and brhuhad gayatri. She is the adhidevatha of Gayatri mantra and the sandhya vandana. On the fourth day of Navarathri DEVI is decorated as GAYATHRI DEVI, the Pranava Swaroopini, who is the source of NADA, She is the soource of Sakala mantras, and she is the source of all vedas. The inner meaning of this Alankaram is that DEVI protects the universe in the form of Annapoorna and she grants the PRADHAMA BHIKSHA to the AADI BIKSHU SIVA and she strives hard to protect the universe by providing food so she shows that the best DAANAM is ANNA DAANAM and who ever donates food is a form of that DEVI and let us follow the footsteps of DEVI and do NITHYA ANNA DAANA. And this devi resides forever in the SMASANA BHOOMI called the KASHI and she is the divine consort of VISHVESHWARA who is the father of this universe. On the third day of Navarathri Kanaka Durga is decorated as ANNAPOORNA, Annapoorna devi is the one who provides the ANNAM ( the food ) and maintains the lifecycle of not just the creatures on this earth but of the whole universe. Satya lakshmi, Bhoga Lakshmi, Rajya Lakshmi, Yoga Lakshmi, Vidya Lakshmi, Soubhagya Lakshmi, Amrutha Lakshmi, Kamya Lakshmi are the main Avataras of DEVI besides the famous ASTA LAKSHMI avatarams. She is greatly praised and her significance is given in details in SRI SUKTAM and LAKSHMI TANTRA. Second Day, Kanaka durga is decorated as MahaLakshmi, Mahalakshmi is famous for her DHAIRA quality, she did play a vital role in MAHISHASURA mardhanam.