Pool, I believe - the purpose of the chlorine and other additives is to kill the nasty germs you would otherwise find in fresh water. With lakes and natural bodies of water being usually stagnant and polluted in (and full of parasites, bacteria, chemical runoff and dumping, and debris), I would think a pool is safer.
I grew up swimming in pools, and though I have asthma and allergies (seasonal), my mother and grandmother also have allergies (grandmother has asthma too) and they have never gone pool-water swimming much at all, if ever (grandmother, never).
I would also have to vote for a pool...if you're worried about the cholorine, lakes and streams have chemicals in them too (runoffs from farmland, etc.) so they aren't any safer when it comes to avoiding them.
I've never had any problems with the lakes we've been to. I prefer them over pools. I can't swim in indoor pools either, the chlorine buildup in the air makes it so I can't breathe and I don't have asthma or allergies.