Is it normal for a green anole lizards tail to fall off?

Yes. Green anoles are just one of thousands of lizards that can regenerate their tails. Their tail muscles spasm, and with a little extra tugging, one of their tail vertebrae fractures at its weak point. The tail will never be as good as the original; with bones made only of cartilage and probably growing back less that picture perfect, but it's a life-saving tool that can be repeated indefinitely.