If I were you, I'd contact the The Green Mountain Club. You can buy the most recent trail guide and as others have mentioned, that's really your best bet. Also, they actually have a list of people who have completed the trail who can offer you advice and ideas.
I agree that July/Aug/Sept is typically the best time of year to hike the LT. Most years, June is very wet and rainy. When I hiked most of the LT a couple years ago, June was perfect, but Aug and Sept were great too.
I live in VT and have spent countless hours on the LT over the past 10 years. I'll be on the LT this weekend. If you have any questions, I'd be happy to help you.