He can separately apply for a LAPL, for which his Class 1 Medical is already valid with an SEP rating on it
No - he cannot.
EASA do not allow pilots to hold two Licences (for the same category of aircraft) so he can have
either an LAPL(A)
or an ATPL(A) (which already contains LAPL Privileges within it).
NB:
An LAPL does not contain Ratings. An LAPL(A) would allow flight in either an SEP or a TMG, depending in which aircraft the Test was taken. The privilege to fly the other Class may be obtained later, following additional training.