He was possessed by Morro before, so he knew what it was like to feel two contrasting identities inside fighting for control over himself. When he sees Harumi, he notices that her actions to save him and her motivations to destroy the lives of everyone else are inconsistent, revealing the internal battle within her he recognizes all too well: the side that embraces goodness v.s. the side that wears the mask of trauma, hatred, and revenge. So he tries to reach her, because he would've been consumed by his own internal battle if not for being rescued by the people who loved him.
Morro's possession is only one of Lloyd's many internal battles. He has Dragon v.s. Oni instincts, accepting connection and harmony with others v.s. being consumed by his doubts and self-loathing, revisiting a lost childhood v.s. facing adulthood, maturity, and the responsibility the world needs from him, following his calling v.s. rejecting it to choose his own happiness, and probably more that I'm missing because there's just so many. But despite the exhaustion from dealing with these battles and wanting to give up, he perseveres. He perseveres, so he can reach lives like Harumi's, who are suffering from their own battles. He perseveres, so people like her can be free and find peace. Because he knows what it's like to barely survive battling himself, and he doesn't want anyone to experience what he goes through.