The recent vote by the EASA committee will mean that LAPL privileges will now be included within PPL privileges and that the validity of the pilot's medical will be the deciding factor. Thus the holder of a PPL with a valid SEP or TMG Class Rating, whose Class 2 medical slips to LAPL medical standard, will simply be required to operate aircraft which are within LAPL restrictions (VFR, max 2000kg MTOM, max 4 PoB). But this change has not yet appeared in law and will probably only come into effect later in the year.
Part-FCL does not permit a pilot to hold 2 licences for the same category of aircraft.