I'm almost a proponent of solid studs. That way you don't care where the rails get mounted. Don't forget that most elevator manufacturer's (at least around here maybe we're getting shafted) want a full shaft width opening at the bottom and top floors for cab install. So you don't actually have a shaft wall there for lateral, but you likely don't need it if your corridor walls are all wood and are continuous down to the foundation.
Thanks,
There is an access opening at the bottom. They dont call for full opening, only a beam a the top, thats for the rails to connect and a hoist beam, and then they have clips at floor levels.
I've done a wood framed 5 story elevator shaft before. Didn't hear back so I guess it worked. LVL's turned sideways for the rail supports (LVLs both for strength and to limit shrinkage). Typical stud framing for the rest of the shaft. One wall of the shaft was exterior brick, existing; so that helped. Shaft wasn't used for any lateral stability. Sheathed the shaft in gypsum for fire protection and used the gypsum for general stability of the shaft but mostly relied on the LVLs for rail stability. Sealed up the gypsum where the rail penetrated the gypsum into the LVL (plus considered the flat LVL as something unlikely to burn through quickly).
Here's my final design if you want to borrow some things:
