Booking system for shows
Structure

Generally, a method should do one thing. For example addPlay should add a play (although it's an odd method for a play class, as a play generally cannot own another play). But your method doesn't just add something, it actually retrieves user input, prints stuff, writes stuff to a file, and then calls a seemingly unrelated method, which asks for more user input and processes it in some way.

It's also very unclear what your LocalPlay class is actually supposed to do. Looking at the fields, constructor, and getter/setter, it looks as if it holds the data for one play, but then it is also possible to add a play, which doesn't make sense. 

You should definitely try to separate the holding of the data from the parsing of user input. 

You should also try to better define the tasks and differences of lPlayDetails and addPlay, and you should try to remove the confusing call structure (the functions call each other, which makes it difficult to follow the control flow of your program).

Misc


there is no reason to make the fields (or the methods) static. 
your naming is a bit confusing. There doesn't seem to be a difference between a play and a show, you seem to be using both interchangeably. In that case, use just one of the terms for clarity.
if a method is not implemented, it shouldn't do anything. Instead of doing something totally different, throw something like an UnsupportedOperationException. 
lPlayDetails: It's very unclear what this method does. The name is vague and it is missing a JavaDoc comment. It is also very unclear what the exact difference to addPlay is.
it is very unclear to me why you create a new LocalPlay in addPlay. There doesn't seem to be a reason for it, and it seems to be unused.