The hammer pivot is considered part of the hammer itself, though it seems to be a separate pin inserted as a press fit through the hammer itself.
You can remove the hammer from the lock, carefully marking the depth the pin needs to be with a simple scratch mark before driving the pin itself out altogether.
Just remember/mark which end is which on the pin.
Clean the surfaces and a touch of locktite to them and tap it back in place to the mark. Wipe any excess off and let it cure.
Reassemble the lock.
If you don't want to do lock disassembly (and they are actually very easy on the LCS)..
If it keeps disappearing into the lock from the outside, you can locate the position opposite the pin on the inside w/a bit of careful figurin'. Then glue up/re-bed the wood in that area to support the pin and bridal so it can't back up on you. They should be bedded that way anyway but many are done by the mining & excavation method leaving a void behind them and room to move back in.