I don't want my girlfriend to go out to eat alone with another man
That sounds controlling. Why don't you want her to go?
Because I love her with my whole heart!
She is a lucky girl to have someone who loves her like you do, but you shouldn't dictate who she can eat lunch with. If you are too restrictive, you might drive her away.
I love her so much. She's the light of my life, my soul mate, my everything.
If you really love her you need to let her have a life of her own as well. This will only cause trouble telling her what to do like that.