Lilly Belle has been running almost daily since the start of the 60th in May. I've had the good luck to do it twice in the last couple of months (including Wed. July 15). At park opening, go straight to the Main Street train station and line up left of the front doors (when facing them). At 8am a conductor will let you know if they are running tours that day. Note that if rain is definitely in the forecast they won't run tours, and tours may be canceled if it starts raining or if the temperatures go above 80 degrees (no A/C in the car, just a small fans and whatever breeze comes through the half-open windows). The car can seat a maximum of 14 people. It's first come first served, and if they have to cancel, you don't get anything for your "wasted" time. If the car is running that day, the conductor running the tours will come out at 8am and let you know how many tours they plan to give that day and the times, and then will go down the line and take reservations. One person in line could be making reservations for larger groups of people, so don't rely on a head count to ensure your ability to ride that day. They don't usually make standby reservations in case of no shows, so don't count on that either. The earliest a tour might start would be 9am on a day with an 8am opening. I've heard they've done as many as three tours a day on cooler summer days.
If you are lucky enough to get to ride that day, return at least 15 minutes before the scheduled time. If everyone is ready early and the train with the LB car comes into Main St Station, you'll board it early, otherwise, your group may have to wait 20 minutes for it to come back around. If you are late, they'll board without you. Each member of your party will get a souvenir ticket. If you know you are going to try for the Lilly Belle during your trip, it might be a good idea to bring something to keep the ticket(s) from getting bent (a cardboard envelope/mailer is a good option). The train car is lovely, the seats are very comfortable, and the conductor has a wealth of information and Disney trivia to share during the trip. You can take pictures during the trip, and they will often take pics of you in the car when stopped at the stations. No food or drink or anything messy or wet is allowed inside. It can get a bit warm inside the car, so dress accordingly. Those with mobility issues will need to be able to climb the three small steps from the platform to the car. The tour is 20 minutes, round trip from Main St Station. You can not get out at any other stations (platforms not long enough), not that you would want to.
Good luck!
in a few weeks...but it will be hot-does that matter? Someone else mentioned a place to 'sign up' to ride-true??
They really enjoyed talking to the CM on the ride, she was full of fun trivia, some that they knew, some that they didn't Both times we were lucky enough to ride we got there first thing in the morning (after MM, never during) and asked if the LB was running and if there were reservations available. We asked many times but we were only lucky enough to ride it twice. You may have to try multiple times but keep trying and eventually you'll get to ride. 
