I think its to help prevent the horse from messing with the shanks and it also stops you from losing your curb chain! I always use one but I'm not sure about it being correct...
A lip strap on a weymouth stops the shanks 'inverting'. (FMM has a very impressive link showing the effects of this), and the lip strap on a pelham stops you from losing your curb strap if it comes undone.
Not everybody uses one as some people feel that it clutters up the horses head. I use one for a.'correctness' and b. because a judge once told me off for not using one - I need all the brownie points I can get out of judges - hence I use a lip strap
It also helps to keep the curb chain lying flat in the chin groove so when the chain comes into use its the flat side that works correctly rather than the chain twisting and nipping the groove/skin etc....