[X] Explore the Secretive Parts of the Lab - Exploring the rest of the base would be interesting and you may run into other Rockets hiding down there. It'd be useful to see what they were working on.
[X] Claim the Base - Technically this base isn't owned by anyone. And Willow and you did take it over. You're not sure about the legalities, but it sounds like that makes it yours. See if you can formally claim it.
-- [X] And loot everything inside not nailed down since by proxy of you owning the base all its contents are now yours as well. There might even be some TMs or battle items in here that we can use in the Indigo League.
[X] Interrogate the Rockets - Surely some of the Rockets would be willing to talk? The one that confronted the three of you is very selfish and quite likely to turn on their colleagues.