“Stapler” means “stacker” and “forklift” means “Gabelstapler” which is “forkstacker”, but it’s abbreviated here. And yes, “Lager” is storage :)

I think in this case I would translate “Lager” as “warehouse”

and lager really mean storage

Yes, but can also mean a camp, a type of beer, a resource deposit or a ball bearing (and probably more).