If we are talking about an invitation (English) or an invite (American) you can use either 'to lunch' or 'for lunch' although 'to lunch' might suggest we are going to 'eat out' somewhere, and 'for lunch' might suggest eating at the inviter's home.
I would not invite myself so it might be a impolite to ask if can I come 'for lunch' if I have not been invited first.