No, just as a PPL/FI may instruct an ATPL holder for the Aerobatic Rating (assuming he/she holds the relevant qualifications, a LAPL-level FI may provide flight instruction for a Night Rating to be included in a pilot licence, again assuming that the relevant instructional qualifications have been met, irrespective of the licence level.
It is only the instruction for a licence, not a rating, which requires the FI to hold the same (or higher level) licence. Thus a PPL/FI may not instruct for the CPL itself, but may instruct a CPL holder for an additional rating - and the same logic applies to the 'LAPL/FI'.
EASA made this clear several years ago.....