We did a great ~8 mile loop hike last year from Beartooth Lake that went by several backcountry lakes.
We started at Beartooth Lake and headed N/NW parallel to Beartooth Butte. We met up with the Beartooth High Lakes Trail and started turning more to the east. This trail gets you pretty close to prominent Lonesome Mountain if you want a summit diversion. The loop we took continued on to Claw Lake and turned south toward Beauty Lake before returning back to Beartooth Lake.
I don't remember the names of all the trails offhand, but looking at a trail map, the loop is pretty obvious. We didn't fish, so I can't speak to the quality of the fishing on the lakes. We were there mid July last year and encountered numerous stream crossings (calf deep) and boggy areas.