Just to clarify, are you looking for a hair stylist or a barber? I know there's a place near the top of Chemin des Croix Rouges
(on the right-hand side heading down from Pont Chauderon) run by an an English-speaking African guy that you could go to for barber work (e.g. a number 2 all around) or probably a basic guy's cut, but if you're looking for a stylist I'm afraid can't help.
As a warning, expect to pay at least three times as much as you would in Canada. I remember back in Waterloo I used to think $20 for a haircut was extortion, and now I think $50 in Lausanne is lucidrously cheap.