The Lilly Belle is a special carriage on the back of one of the trains on the Railroad.
It is not run every day and does not technically provide you with anything special over a standard trip on the railroad.
It was built by Walt Disney for his wife Lilly (hence the name) and is still decorated as she had it decorated.
It is not something that you'll need to plan for in your touring plan, so long as you have included time to ride the railroad.
Having said that, I believe it's quite rare to be allowed to ride it and you have to be lucky (I have been fortunate enough to have the privilege). It is normally an honour reserved specially for Club 33 members, although in the past, City Hall have authorised the occasional person to ride it who has asked them nicely. If you are allowed to ride it, then you must do so with a CM accompanying you (nobody is allowed to ride without a CM).
It is an amazing, humbling experience if you are allowed to do it in my opinion, but is not something you should plan or expect to be able to do as it is a privilege given to a lucky few at the discretion of City Hall rather than an "automatic right" granted to anybody who asks.