Until the age of 21 I was right-handed. Since then, owing to an accident, I have had to be left-handed.
Some things that would be more convenient for me on your left-handed lathe:
sliding the tailstock along the bed and probably all other manipulations of the tailstock apart from inserting or removing drills etc.;
Cranking the compound-slide handle.
Some things that would be less, not more, convenient on your left-hand lathe:
locking and unlocking a typical jawed chuck;
Inserting and removing drills etc. into and from the tailstock quill;
Accessing gears or other things inside the gearbox casing;
Operating the on-off switches, speed-control dials, quick-change gearbox levers et al.
It's not lathes where I really feel the need of a left-handed machine, but mills and drills, since cranking a right-located handwheel to raise and lower the head, cranking the x-axis handwheel on a milling table having a single [always right-positioned?] handwheel, and lowering the quill [coarse feed on a mini-mill] are genuinely troublesome for me, especially the first two of these.