I am going to be start running LOF with PF 1 and looking which books are the weapons the templars are located in so far seen seen first 3 are in books 1 and 2.
Pathfinder Adventure Path, Lost Omens, Rulebook Subscriber
As you mentioned the first 3 weapons are in books 1 and 2. I you don't see another weapon until book 6. I believe you never see one of the templar's weapons. I think they talk about what the weapons are supposed to be in book 1.
The party I going to run are Unchainned monk, UC Rogue, Life Orale( GMPC), Witch just waiting for 1 more before I start running as if the pc defeat former templars in battle or convince them that it time for new templars sunder their weapons to the PC.