Good point about walking into Tower from the East Two. I often forget about that.
You could also go to Glenwood Lodge at the east end of Pine Island. It's mostly beer and pizza with snacks, at least the last time that I was there. As far as I know, what Skibo and I posted are all of the locations on or near the lake.
There are also multiple shore lunch sites on the lake. They all have beautiful views, a picnic table, fire ring, and latrine. Bring your own lunch, or better yet, bring the fixings to cook up your fresh catch from the lake.