I've been playing for a while now without unlocking any new items for my secret lair (mainly looking to build a trap corridor, but really lacking in traps). Are item/room/trap unlocks based on notoriety, loot, acts of infamy, or some combination?
A number of items are unlocked via the story when new types of heists are made available (most of your loot items are gotten this way) but for new types of rooms and utility objects, you'll need to do research.
Research automatically becomes available via the storyline -- you'll get a possible heist to steal a highly advanced research machine, then need to fool the agents into stealing a fake research machine back, and acquire several experimenting devices (three of six possible; you get new opportunities for the remainder later).
(Those experimenting devices also make for hilarious agent torturing methods, btw. Be sure to put them through their paces from time to time. :) )
Once you have the research machine and the experimentation devices, make sure you have idle scientists of various types. They'll meander around your base looking at stuff you have built, then poke their ideas into the research machine until research combinations pop out that you can tell them to start working on. A while later, a new design will pop out.
A full list of what combinations result in what can be found here.