Shua, state fishing licenses are required in all states in which I've lived (and that's over half of them). The only exceptions are in a very few national parks (such as Yellowstone) that were established before 1900, before modern game laws. National forests, which are a 20th century phenomenon, are not exempt from state game laws. In addition, the OP plans to hike the Appalachian Trail, not the PCT, so info on Washington lakes won't help much. (Now if you want to share that info with me…. )

Wclary, as others have mentioned, the Appalachian Trail is so crowded and close to "civilized" country that there is no way you'll find sufficient forage. Plus it follows ridge tops, so you won't be close to potential fishing areas for much of the trip. Lots of ponds at the Maine end, but by that time you'll be in a hurry to finish your hike before the snow flies!