LPC won't suffice, as mentioned you need an LST, whihch in effect is a couple of extra items (including hand flown raw data ILS) and a couple of extra bits of paperwork (see LASORs). I wouldn't have thought your new company will balk at including these in your initial LPC for them. Takes an extra 5mins and a little bit more box ticking for the TRE. However it does cost to change CPL to ATPL, so check they will pay too!