I have not mounted them on my sailboat - yet, but depending on your layout, I'd put them about 3/4+ of the way back in the cockpit, or just aft of a rear traveler. You will probably want to "troll" via the jib and have the boom up and out of the way via a topping lift...
Welcome to the forum. While unfamiliar with lake fishing, I do have some salt time. We use a 6 spool gurdy system with 65 lb canon balls to fish commercially for salmon. There is no reason that you cannot employ a down rigger to troll for fish while under sail. I have done it for years.
" Wisdom; is your reward for surviving your mistakes"