Her evidence is that morality is widely varied throughout the world and in each context. That if it was real, it would have a more uniform set of tenants to point to its existence. Since it is different in every time and place, it simply doesn't exist. It's made up.
There's a few things to pick apart here.
Firstly, the assertion that morality varies is challengeable. There are ways around this, citing common ground between many religions, etc. This is actually often a case made by atheists ad there's plenty written on it.
However let's say that it's given that morality does in fact vary, why does it's variance make it "made up"? Why can there not be many moralities? Lucy would have to have the position that for morality to be "real" it must be universal, and so reject the idea of moral relativism. My only point here is that it is not easily dismissed and has been debated for thousands of years.
"Made up" is a put down of the highest order. Is music "made up"? Are numbers "made up"? I guess the idea here is something that exists outside ourselves, perhaps that is the only think which is not made up. Here is where the idea of morality very much rests on belief in a God because what else so concerned with human ideas could be relevant.
If I were in your shoes I would probably add to the Texan nerd stereotype the idea that they are deeply religious, probably messing with you for fun.