iMHO it is prefectly possible for the turbolift to be centered and the entrence to the turblift to be to the side.
In The Nitpicker's Guide for Classic Trekkers, Phil Farrand, 1994, in the section on Star Trek V: The Final Frontier, Equipment Oddities, page 367:
What's more, not only has the designation for the turbolifts changed, they have actually moved! Prior to this movie, there was one station between the turbolifts. Now there are two. Bear in mind that these turbolifts travel in tubes. You can't just move the doorway: you would have to tear out the entire tube, shove it over, and then rebuild every deck it intersects. Does that seem reasonable?
In the Equipment Oddities section for Star Trek VI: The Undiscovered Country on page 375, Farrand says:
And speaking of the refit, why in the world would the designers move the turbolifts again? (See the previous movie) Are they trying to find things for the workers to do? This movie shows several stations between the turbolift doors.
So after reading that I eventually decided that the two turbolift doors on the USS Enterprise NCC 1701-A did not mark the locations of the turbolift shafts. My theory is that the turbolift shafts rise vertically to the level of the bridge, and then turn right and left to reach the positions of the turbolift doors.
And since one solution to problem of all the changes made to the Enterprise NCC 1701-A bridge is the replacement of one entire bridge module by another entire bridge module, it is possible that different bridge modules have different lengths of horizontal turbolift shafts leading to the differently located turbolift doors.
So my theory is that the TOS starship, the USS Enterprise NCC 1701, also had a turbolift shaft which rose vertically to the level of the bridge and then turned horizontal for a distance to reach the turbolift door. It is possible that the horizontal length of shaft leading to the door on one side is mirrored by another length of horizontal shaft on the other side holding spare turbolift cars.
Thus it is possible for the turbolift shaft and the viewcreeen of the TOS starship, the USS Enterprise NCC 1701, to both be on the centerline of the starship.
Or it is possible that the thing seen behind the bridge dome is not the turbolift shaft head but something else, and that the turbolift shaft machinery doesn't stick out from the surface of the bridge dome. Thus the turbolift shaft could be to the side, and the Viewscreen could face forward.
A similar question is asked at:
https://www.trekbbs.com/threads/is-the-bridge-at-a-funny-angle.306619/page-9[1]