The most common unlined jacket is one where just the back is unlined This would be the easiest conversion to make and the suggested one.
If you look carefully at a lining, you'll see the seams parallel the ones on the jacket. At each side seam you would snip the lining, bottom upwards, parallel to the seams, but about an inch beyond, toward center back, giving you a margin to fold the vertical edge of the remaining lining under and tack over the jacket's seams. Tack, which is to lightly sew, the seam of the lining to the seam of the coat. You would do this on both side seams, then you would remove the back lining, after making a horozontal cut approximately 6 inches from the top, folding the still attached remainder under for half an inch and sew to itself. This back liner piece flows free, air can circulate underneath, almost like there was no liner there, but it has to be there because it lines the yoke, else the jacket would stick to the shoulders.
This is the type of conversion that a tailor could certainly do. I have done this. It is not difficult, does not require much skill, but does require care, patience and time. Ball game on the radio helps.
This next paragraph of yours I don't fully understand.
I hear the lining is not actually attached/connected to the canvas – does that mean would it be possible to do a liner-ectomy losing not much more than the inside pockets?
You could remove the lining past the side seams clear to the interior fabric at the front of the jacket, canvas is under this strip, seldom extending to under the lining. But then you would have to finish off the newly-exposed side seams, possibly with a blanket stitch, usually with binding/piping. Canvas floats free to a degree, it is lightly tacked at maybe a half dozen random spots to the jacket, only so it doesn't bunch.
The conversion you desire is certainly possible, particularly if it's on an expensive or a favorite jacket. It is a hell of a lot cheaper and easier to do than buying a whole new jacket (unless maybe you're buying second-hand). Not fixing up what you already have is always my last resort. Buying anew, pretty much frowned upon.