The problem lila answers, why a complete being would create at all, is not unique to Hindu theology, and comparing how Western theistic traditions handled the same problem shows both a shared puzzle and a genuinely different solution.
Classical Christian theology, developed by Thomas Aquinas, faced essentially the same difficulty: since God is perfect and lacks nothing, creation cannot be explained by need, and Aquinas's answer was that God creates out of the sheer overflow of divine goodness, which by nature diffuses and communicates itself, so creation is a free gift rather than a filling of lack, closer to an artist's gratuitous expression than a laborer's response to necessity. This is close to lila's insistence that divine activity has no external motive, but the traditions differ in tone: Aquinas frames the motive as generous self-communication, a solemn act, where Hindu lila theology, especially in its Vaishnava devotional forms, frames the same activity as play and delight, closer to a child's spontaneous activity than a philosopher's account of overflowing goodness.
Process theology, developed by thinkers including Charles Hartshorne working from Alfred North Whitehead's philosophy, offers a different answer by rejecting the premise both lila and Aquinas share: on this account God is not complete and static but is enriched by an ongoing creative relationship with the world, so creation answers a real divine interest in increasing value rather than being purely gratuitous activity, a solution classical Vedanta and Thomism alike would reject as compromising divine perfection, but one showing the question admits genuinely different answers depending on how strictly completeness is held.