Yes, but organisations providing LAPL(A) training will need to be EASA-approved ATOs. Which is likely to be expensive (very!), so why would they bother? They can still provide PPL and NPPL training as RFs for a couple of years yet without having to pay rip-off CAA ATO approval fees.
Unless we manage to retain RFs for PPL-level training, the LAPL(A) may well wither on the vine....