I did the LT last year north bound ending on October 10th. You will have a great time but, here are some things to expect
I had a very wet hike, some form of precipitation 20 days in a row.
Expect snow, 4 inches on October 1st
There will be very few other hikers
I didn't believe people that the northern section is rough, it is. It is bad. Really bad. Really bad.
This is my gear list for the trip
I ended up using a warmer sleeping bag, and would have switched the Patagonia r1/down vest for a lighter long sleeve/down jacket. Also goretex socks would have been very useful.