DD,
Are you going to Farnborough FS? If so, speak to them as they are quite familiar with the LSP/LPC deal.
There's a couple more items you'll need to get checked for the LST on top of the LPC but it's no biggy. Call them.
From what colleagues have told me, FS in the US have had some paper work issues with doing LSTs for the unfreezing of an ATPL. So, a colleague did his LPC in the US and had to go to Farnborough to do the LST.