My boyfriend is a sweetheart but lies over trivial things. Is it worth it to stick around?

since we've been dating, my bf has gone above and beyond and is a total gentleman. He's funny, smart, charming and sensitive. But sometimes he lies about where he's at, for little to no reason at all. He always needs to know where i'm at and seems to think i'm going to leave him. Yet when i confront him about his lies, he claims i'm overreacting. he promises to work things out, and everything turns out ok for a week or two. he often overyzes what i say and takes it in a bad way. he's a huge sweetheart but his insecurities, clingy behavior and senseless white lies make me reconsider being with him. is it worth it?