1000 names of Lalitha Devi is mentioned in Lalitopakyana in Brahmanda Puranam. This is advised to Agastya Muni by Hayagriva.
श्रीब्रह्माण्डपुराणे उत्तरखण्डे श्रीहयग्रीवा अगस्त्यसंवादे).
Hayagriva explains about Lalitha Tripura Sundari. Once Lalitha Devi called all Devatas to compose a Hymn containing her names and greatness.
Thus Vasini & Vak devatas composed the Lalitha Sahasranama consisting of the most secret mantras After composing, they all chanted Sahasranama before Lalithambikai.
Pleased by this Devi blessed them, whoever chants this will obtain my favor, wishes of them will be granted. Regular chanting is as beneficial as visiting religious places, taking bath in holy river.
Those who recite Lalitha Sahasranama on Fridays will receive blessings abundantly. Chanting Devi’s name once equals chanting Shiva’s name thousand times, which itself equals chanting Vishnu’s name.
In homes where this is chanted regularly there will Lakshmi Kataksham always For those who are affected by Rahu dosha or to whom Rahu Dasha is running chant Lalitha Sahasranamam during Rahu Kaalam on Tuesday & Friday by lighting a ghee lamp at home
Devi is Navagraha nayaki. Tuesday Rahu Kaalam is 3 to 4:30 and Friday 10:30 to 12.. Light diya using ghee and chant Sahasranamam.