We hiked the Gulf Hagas trail (about 8-mile hike roundtrip from LL). We stopped and turned around at the point where Gulf Hagas intersected with the AT. But as folks have said, you could drive from LL to get closer to the AT. The folks at LL are great, too, at helping you pick out hikes and trips depending on what you're looking for.
Very close to the turn into the Little Lyford area is a connector trail which you can use to access the AT in the 100 mile wilderness. You have a mile or two hike, I believe, from the connector trail to the AT off the Katahdin Ironworks Rd.
Forgot to mention that Monson is 20-25 miles from LL.
The actual Appalachin Trail is only 5-6 miles from Little Lyford. There is a parking lot and good entry point at Monson, Maine. There are other entry points closer to Little Lyford you can go to also. Get a map. The maps are really good.
Get an answer from AMC Little Lyford Pond Lodge and Cabins staff and past guests.