It makes no difference whether the FI is restricted to LAPL training only or not. If a student starts on a LAPL course, he/she must complete the course and obtain a LAPL before he/she may convert to PPL.
That's because, despite earlier assurances, she-who-must-be-obeyed at EASA has now dictated that no LAPL training credit towards the PPL will be extended to a pilot who does not already hold a LAPL...
Nonsense, I agree.
So students need to know that, as far as the LAPL is concerned, they may not change courses mid-stream.... (If that can be proved, of course!)