The bigger picture is that Part-FCL only considers Part-FCL licences. As the 'LAPL-only' FI may not provide any instruction for holders of SEP Class Ratings, there is no need for 'LAPL-only' FIs to have FCL.945 privileges because no entries are made in a LAPL - there's nothing to sign!
Of course in the UK, instructors with FCL.945 privileges may also sign revalidation entries in NPPLs, but that's of no concern to Part-FCL per se.
Assuming a 'LAPL-only' FI also meets the prerequisites for a CRI certificate, then such an FI should certainly apply as Whopity suggests.