I want a set of Imperial Legion Armour, yet every time I have gotten myself a set, it always involves killing a soldier, which I don't like to do. Is there anywhere in the game where I can get the armour set without stealing it or killing its owner? Best part of a decade and I never bothered to find this out....

AFAIK, there's no way to get one normally in Vanilla.

There's an armory in the IC prison where you can steal a set. Otherwise you can only ever get it from dead Legionnaires. You can lure them to their deaths or something or loot them off one of the soldiers that help you during the optional Kvatch quest in the MQ (they're prone to dying).

If you like the look of the armor that Imperial Legion Foresters wear you could hang around them for awhile. They have a bad habit of attacking each other. You might get lucky and be able to loot their armor without killing anybody.