I think I figured how Wilzig knows all this stuff about Lucy, including her actual name!
It's not like Wilzig randomly decided to steal the cold fusion. He and Moldaver must have met before and decided upon this entire plan. She must have told him about Rose escaping with her kids, Lucy and Norm, from Vault 33 back in 2077, Hank MacLean coming to take them back, and the subsequent bombing of Shady Sands. She must have also told him she intended to kidnap Hank to get the activation password out of him.
So when Wilzig meets a young woman from Vault 33 (the number is displayed clearly on her jumpsuit) who is looking for her father (she mentions this when they are in Filly) who was apparently taken by none other than Moldaver he just puts two and two together. He figures out who she is. This is why, just before his death, he addresses her by her full name.