Further to BB's post, LAPL instructors do not require CPL theoretical knowledge and yet will still be eligible for remuneration, which means EASA is not toeing the ICAO line on this one. Mind you, it's a sub-ICAO licence.
So, as it stands, Teejamn and Stupix, yes, you will need to pass CPL theory exams unless you just want to teach the new LAPL.
Regards, jez