I'd lend a fixed bike to someone who was used to riding one, but not to a novice. They take quite some getting used to, and I think everyone has a few minor crashes in the first few days of riding fixed. Chances are I'd get a bike with more scratches and dinks than the one I lent out.
Best bet is to buy yourself a cheap old bike and fit a fixed rear wheel to it. You could probably be up and running for under a hundred.