Hi! My friend tells me that our purpose in life can't be to be happy. Either one of the religions has got it right, and there is a deity or deities, in which case our purpose is to serve them, or there is no God, in which case we have no purpose other than one we arbitrarily decide for ourselves to follow. Does that claim hold water? Thanks in advance for your help!

I think your friend's argument by dilemma leaves out this possibility: we were made by a deity (or deities) principally in order to lead happy lives rather than principally in order to serve it (or them).

Even so, our having been made for the purpose of being happy wouldn't make being happy our purpose. Instruments made for a purpose thereby acquire that purpose (although, of course, they can later be repurposed). But people aren't instruments; I doubt that they're the kind of thing that can be given a purpose, even by their maker. Or at least, because they're autonomous, people can thwart any attempt by their maker to give them a purpose.

Hence I don't think there could be any such thing as "our purpose in life," if "our" refers to people in general. So I agree with your friend's conclusion (although for different reasons than your friend gave): our purpose in life can't be to be happy. Nor can it be anything else.