The collections menu shows exactly what you ask for. Take a look at collections/keyboard/dlcbook_keyboard.lua and you will find that the function you are looking for is called GetCollectibleUnlockStateById and returns a CollectibleUnlockState.
The ESOUIDocumentation.txt shows that CollectibleUnlockState can be one of these three values:
- COLLECTIBLE_UNLOCK_STATE_LOCKED
- COLLECTIBLE_UNLOCK_STATE_UNLOCKED_OWNED
- COLLECTIBLE_UNLOCK_STATE_UNLOCKED_SUBSCRIPTION
Now you just need to figure out how to get the collectibleIds for the DLCs.