You have this backwards. They don't ask for it and then go looking to see what's relevant, they figure out what relevant stuff it has and then ask for it. If they believe and can show it has evidence relevant to a lawsuit, and you have no 5th amendment privilege to assert in it (IE it is not evidence of a crime, etc), then yes, you can generally be required to produce it.

You can certainly try to get it quashed, but if it really does have evidence relevant to the lawsuit, ... yeah you are probably going to be forced to produce it.