Yes you can swim in Norris lake.
I try to go to Norris lake every summer or every other summer if possible when I have time to and me and my family have a good time at Norris Lake.
You can swim, boat and even go out on a boat to a farther off place of Norris Lake away from everybody else and go swimming there.
Norris Lake has secluded coves where you can boat out to and then jump off the coves and then swim and have a good time.
I prefer swimming in lakes instead of public swimming pools because the lakes are much more fun and free as well.