Lakshmi is the goddess of shri, a word covering wealth, beauty, fortune, splendour and legitimate sovereignty at once, and the single most important thing the tradition says about her is that she moves. She is chanchala, unsteady, and the texts are candid that she leaves. A king who rules badly loses her; a household that is filthy, quarrelsome or lazy loses her. This is not a threat attached to the cult from outside. It is the theology: fortune is understood as a presence that can be hosted and can depart, rather than as a possession.
That is why Diwali is principally hers, and why the observance takes the form it does. Houses are cleaned thoroughly, debts are settled, accounts are closed and new ledgers opened, lamps are lit at every doorway and window, and doors are left open at night. The lamps are not decorative in intention; they mark a house as ordered and awake so that she will enter it rather than pass on.
Her iconography is stable across two thousand years. She stands or sits on a lotus, gold coins falling from one lowered hand, the other raised in reassurance. In the Gaja-Lakshmi form she is flanked by elephants pouring water over her from raised trunks, and this is among the oldest attested religious images in India, appearing on early Buddhist railings at Bharhut and Sanchi as well as in Hindu and Jain contexts. She rises from the churning of the ocean of milk and chooses Vishnu, and the choosing is hers.
She is worshipped by Jains and Buddhists as well, and she has no dark aspect and no wrathful form, which among major Hindu goddesses is unusual. Her sister Alakshmi, misfortune, absorbs that function and is sent away rather than served.