Axel certainly was a man of the grey, but I'd say his character across the series has grown quite a bit to a point beyond the grey. Lea has always held friendship in high esteem, and in BBS all he wanted to do was make a lasting impression in somebody's memories because he liked making friends that much.
In KH2, his drive to essentially try to lure Sora in a trap to get Roxas out of him was born from his deep rooted desire to feel what he felt when he spent time with Roxas (and Xion) during the year Sora slept. He was lonely, and sad, and didn't know what else he could do to bring back his first friend in almost ten years that made him feel alive again. He made a promise to Roxas (and Xion) that he'd bring him back no matter what and Axel doesn't break his promises.
When Axel sacrifices himself to save Sora from the Dusks, it was the first time in a long time that he felt that feeling of having a heart like when he was with Roxas (and Xion)...and I think that alone would make somebody loyal to regardless of their previous convictions. Sora's own capacity to love and connect with other people is rather powerful, especially to those of a similar heart and Lea definitely has the same kind of heart.
Lea won't betray Sora, certainly not now. He's already saved his life twice, and probably considers him a friend. He's always been distrusting of the Organization because of his and Saix's own reasons, only listening to orders as Axel because he didn't want to be axed. Lea will probably still do things because of his own motivations, but he's got a heart now and something worth fighting for.