In most contexts Lakshmi is described as Vishnu's consort, which sounds like a subordinate position. In Shri Vaishnavism, the South Indian tradition of Ramanuja and the Alvar poets, it is a doctrinal office, and the question of exactly what it entails split the tradition into two schools that have not reunited.
The shared position is that Vishnu is unapproachable directly. He is just, and a soul that has done what souls do could not survive an unmediated encounter with justice. Shri, that is Lakshmi, is the one who intercedes: she is purushakara, the agent of mediation, who recommends the soul to him and moderates his response. She is not a courtesy title on the temple wall. She is the reason the system works at all, and Shri Vaishnava temples place her shrine accordingly.
The split concerns how much the soul does. The Vadakalai, the northern school, associated with Vedanta Desika, hold the position often illustrated by the monkey: the infant monkey grips its mother, and while the mother does the carrying, the young one must hold on. Some effort is required, and the soul must at least turn and grasp. The Tenkalai, the southern school, hold the position illustrated by the cat: the kitten is carried by the scruff and does nothing whatever, and grace is entirely unearned, since any contribution the soul made would make salvation a wage rather than a gift.
The disagreement extends to Lakshmi's own status, whether she is infinite like Vishnu or an exalted soul, and to whether her mediation is strictly necessary or an expression of his own inclination. Litigation between the two schools over temple rights ran through the colonial courts and into the modern Indian ones.
Anyone who has met the cat-hold and monkey-hold images in a Western book on grace and free will has met a genuinely Indian argument, worked out in Tamil and Sanskrit over centuries.