It seems that gravity can
be created deck by deck, rather than by having a single attractor at the bottom of the ship. At least there shouldn't be any tech reason to prevent this. Whether this is how it's "really" done aboard starships is a different question. But Archer's Enterprise
clearly had a gravity system that could fail on specific rooms on specific decks ("Unexpected"), and TAS and ENT also showed deck-by-deck gravity control in place aboard TOS era Constitution
class ships. And the E-D had prominent "variable gravity area!" warning signs on the shuttlebay walls...
Now, if the artificial gravity is deck-by-deck, would there be any in the vertical turboshafts (or the horizontal ones, for that matter)? Probably not by design. But it's easy to postulate that artificial gravity fields cannot be terminated knife-sharp at the edges, but will always "bleed" a bit over the edge of the deck. A vertical turboshaft would then have "bleed gravity" from the all surrounding decks, and the lift would fall.
Since lifts do
fall on the E-D in "Disaster" and on DS9 in "Crossfire", this seems more or less confirmed...