It depends a little on context. I would probably use the first one, because it specifies that you're inviting the person to your home. (Apartment, by the way, rather than partment.) "You're cordially invited" is a very formal way of saying this, and -- at least in the U.S. -- is more common on written invitations than spoken ones. If you're not giving a written invitation, you might say something like, "I'd like to invite you to my apartment for lunch." I hope that helps!

I think normally we use the word “to” with the word “invited.” So the first one sounds more natural. However, it does sound very fancy to use the word “cordially.” “You are cordially invited to my apartment for lunch. “