Can you use Lost Vacuum to put a card into the Lost Zone if there is no Stadiums or Tools in play?
No, you cannot. Putting a card into the Lost Zone is a cost not the effect, and you cannot play Trainer cards for no effect.
Source: TPCi Rules Team (2023-06-01)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH11_162
SWSH11_162