Question

Would you like Fred and to leave for lunch now? me or myself

Answer 1

Would you like Fred and ME to leave for lunch now?

Step-by-step explanation:

Answer 2

The answer is me. Would you like Fred and me to leave for lunch now? Because if you were to say this without Fred you would say, "Would you like me to leave for lunch now" rather than, "Would you like myself to leave for lunch now". So your correct answer is me. Saying myself sounds awkward and is not the correct terminology for this phrase.
I hope this helps!