The EPA says there is no problem putting the discharge into a normally operating septic system. They also say the 'extra' water is actually helpful. Millions of softener are connected to the septic system but, there are 3-4 states that still ban it. Those states say to use a dry well. And I think your mention of living by a lake goes to polluting the lake which I would be concerned about or polluting your well if you used a dry well or a sump pump.
I say it should go into the septic.