AFCAS TARGET,
Yes, you can use your last LPC for the issue of your ATPL. LASORS indeed mentions that you need to perform a skills test. However if you have some experience than they will accept a LPC. But be carefull because this LPC must be done after you fullfilled the requirements as set out in LASORS. So in your case, the LPC has to be done AFTER you gained your 500 hours on a multi crew a/c.
The training captain who does your LPC needs to fill in section 3 of SRG/1119. Once signed, you take this form including the other forms and 210 pounds to the CAA and you should get your ATPL.
But if you are not sure about the requirements than give them a call or send an email. At least than you know that you don't show up at their office without the correct paperwork.
FT