Na música de Maddona, não há diferença.
Let it will be - deixa pra lá (deixa rolar).
Only that with "let it be" you are talking about the present (in the Beatles´music about what you shall do now and everytime) ; and with ''let it will be" you are talking about what you must do right now, and from now on.
As I said, sometimes (mainly in music) it wouldn´t make a whale of a difference! (context-wise, of course)