Hello, and welcome to New England! LRP is a blast. Very much a momentum track.
For track specifics, including test day schedule, check Lime Rock's website. Their tuning and testing are always on Tuesdays. They are held in the afternoons, usually from 1 to 5 p.m. The price did go up rather significantly. I believe that it's now $275. You do have to have a valid competition license, and all of the proper safety gear.
You are probably aware that they don't race on Sundays, so they run Fridays and Saturdays for everyday events. The track is open by (if I remember correctly) 6 or 7 a.m. Registration is what will dictate when you can get in. You should be able to pull the schedule off of the supps. In the past, track management has allowed people in ahead of time, space permitting. (they have drivng and racing schools going on there a lot)I haven't run there in a year or so, so you may want to check on that. (1-800-RACE-LRP)
For lodging, I recommend White Hollow Inn, a mile down the road. You never actually see the innkeeper there..they tape the keys to the door for you. It has 4 or 5 rooms only, and it's in a beautiful farmhouse style building. There's also the Interlaken Inn a few miles away. They have a resteraunt and bar, and they cater to racers as well.
There's a ton of good restaraunts around that area, from pizza to fine dining. The LRP website should have some listed, but the perrenial favorites are: Italian/pizza/casual - Brother's Pizza in Lakeville, The Boathouse in Lakeville (semi-casual). Dress up with excellent food: The Woodlands in Lakeville, Interlaken Inn, White Hart Inn. There's more, but these have been around a while.
There are two paddocks, A and B. A paddock is the main one, with the resteraunt, main bathrroms/showers, and gift shop located there. B paddock has the gas pumps in it, and more room. They have/are moving the grid to B paddock, so I am not sure how that will affect parking.
The track is staffed overnight, and you can camp there if you choose. Lot's of folks do, and it's fun to wander around visiting the various campsites.
The racetrack itself is rich in history, and very much fun to drive! I haven't been there since they redid some areas this winter, such as the bottom of the uphill. I understand the changes in safety are for the better. (although I would have appreciated green catch fencing so it would blend in with the woods!)
Either car will be fun on this track, and I think you will find the racegroups to be a blast. ITA seems to be the growing field of late, so if you like a lot of competition, this would be the one. ITB has shrunk somewhat, but there are some good, fun drivers in it.
And the NER workers are topknotch. Yes I am biased somewhat, but I've also raced in FL, WI, OH, W.VA, etc, so it isn't total bias. They are well staffed and well skilled.
I hope you enjoy youself, and feel free to stop by to say hi to us if we are there that weekend. We are in ITC, cars # 10 and 11.