What is the connection between unconditional love and enlightenment?
Unconditional love is enlightenment.
In enlightenment, you become love itself, and your ego dissolves into that love. Love, Life, God, Being, Existence are all synonyms, these words all point to the same thing, they all point to you.
This isn’t Buddhahood yet, not the deepest level of realization, but it’s not possible to know Reality without realizing the unconditional love which is Existence and surrendering yourself to it. That’s the level of realization Jesus Christ taught from, it is already very deeply profound. Sometimes it is also called Reality-Consciousness-Bliss, Sat-Chit-Ananda. That is, strictly speaking, not Reality yet, but words begin to progressively fail at higher levels.