Time to get out the forms instructions and dig into the state statutes! Yes, your NV and CA entities are going to have to file in AZ and LA. I'd have to read the forms instructions to know for sure whether and at what level one of the entities can file a composite return; if not, the grantor is likely to have a filing requirement in those states, too.

"How do I make Lacerte produce the appropriate output" is a question that can only be determined once you know what output is appropriate. LA allocates pass-through income, but the return itself requires reporting the everywhere income under LA rules and then backing out the pass-through income to be allocated, so you still need to do all the apportionment stuff. I don't know AZ law off the top of my head, but the forms instructions will tell you the basics.