Are these the correct ones?
I can share mine with you. You can share mine with me.
Your first sentence is good. But the second example is not quite so good because YOU are the one sharing with the other person. The other person is not sharing with you. If you are sharing your lunch with him, you are being generous and kind. It belongs to you....but you are going to share. It does not belong to HIM, so HE cannot share with you.
However, you can both "share" a lunch. You can say "let's share this, because there's enough for both of us"....even though it belongs to YOU. Does that make sense?