The trail to Lost Lake may be a little long for a day hike, but it's pretty easy, and the destination is great. The lake has abundant cutthroat trout and grayling, some fun boulder hopping, and plenty of informal places to camp — although this means you can also see the impact of heavy use, so please pack out your trash and practice zero-impact camping.
This lake gets its name because it can be hard to spot the way back to the main trail, so as you come here, pay special attention to how you'll go back. Choosing a few key landmarks really helps you keep your bearings in this sort of situation.