At least one ATO with privileges to instruct for the FI claims that a LAPL FI can sign a SEP rating on an EASA PPL.
To be able to do so the FI must have FCL 945 entered into the licence. If they have that then they can, but as a FI (LAPL) they should not have it and therefore like all other FIs who do not have it in their licence, they are not authorised to sign a licence for revalidation. A 945 sheet
here: