The lights in a diagonal shaft (in which the turbolift cabin is of course keeping a vertical position!)
But that would mean both that the lights would go past the windows diagonally in the general case, and
that the shaft would have to be wider than the turbolift is. The first would be contrary to evidence (or indicate complex rotations for no obvious purpose other than hide the angle of the lights passing), the second would simply be inconvenient. We know that tiny spaces such as shuttlecraft can easily be provided with gravity independent of outside gravity or accelerations; tilting the turbolift would be a possible solution, then, and it would definitely be a sensible solution.
Indeed, it would make some sense to have the lift tilt to horizontal as soon as it departed a station, any station - the shaft could then be of a smaller cross section and consume less precious inboard volume. But admittedly the TOS lift cabs do not diverge all that much from spherical, unless there is major machinery atop or below that we are unaware of. Tilting of this sort might not create much of an advantage, then.
I think they would put it to better use by displaying a ship's schematic that tells the user where he or she is (compare TMP).
One might indeed speculate that the lift panels have this very function - but that the function is hidden for aesthetic reasons, just like the interfaces on Enterprise
-D corridors remain dark until called forth. By the time we joined Kirk and his crew, these people would be so thoroughly familiar with their own ship that they would never call forth the shaft network map.
So we might be looking at various turbolift cabins, too - small or big - especially since we have never seen the inside of a TOS turboshaft.
Again strongly agreed. The more diversity in the range of cabins, the farther we get from the limiting idea that the lift system resembles those of today, and the closer we get to the idea that the ship has internal "roads" along which various "vehicles" travel.
No doubt there could exist a dedicated ambulance cab that not only accommodates stretchers (horizontal or vertical) but also provides various medical support services to keep the patient(s) alive till they reach sickbay. I could also see the need for fairly small logistics cabs that deliver objects down to the size of document folders or food trays; these just happen to exit the network through different, dedicated smaller hatches. As for shaft size, it might be optimized so that two (Or three? See ST5) "standard" turbolifts could just barely pass, while special vehicles would take up more room and shove other traffic aside.
...Essentially, the shaft network would be much like what we see in Wall-E
, with robotic servants of all sorts moving back and forth (and up and down and sideways). Only a tad more orderly and subdued, as this is
a heavy cruiser rather than a pleasure cruiser.