As well as knowing exactly what to say, also be sure to have a good idea in your head what you expect them to say in return. If you know roughly what to expect, it's a lot easier to assimilate that information.
I've never flown into LPL, but from experience of other class D airports, I would expect them to clear you to enter the zone via a particular report point or entry/exit lane at, or below a specific altitude. For example, if approaching from the SW, you COULD expect somthing like:
G-xx is cleared to enter the zone via the Chester VRP, not above 2000ft nnnn(Mb), remain east of the M53 and report abeam Chester.
Finally, get a copy of the Local Flying Entry/Exit procedures from the NATS website
here (regsitration is required and free) and study this before you go. Having copied the ATIS, you'll already know the local QFE and runway in use, so you'll know exactly what to expect when you make that first call.