To fly with an LAPL medical you require an LAPL licence. A full PPL cannot be used with an LAPL medical even with restricted privileges. This ludicrous situation has allegedly been under review for several years.

There are changes in the pipeline to address this issue and allow a PPL to be used with a LAPL medical to give LAPL privileges. The earliest this is likely to become law is about July 2019, if the relevant package gets a positive vote at the June EASA Committee..

Denmark has already implemented such a practice through an interpretation of the wording of FCL.040/MED.A.030, as per AIC B 06/17, later revised through AIC B 09/18:

https://aim.naviair.dk/media/files/yv4ebrkjv2c/AIC%20B%2009%202018.pdf

This practice was implemented, even though the [previous] wording of MED.A.030 (c) could be interpreted in such a way that a PPL(A) holder would require a class II medical, regardless of privileges exercised.

With the implementation of the revised Part-MED earlier this year [regulation (EU) 2019/27], I would think the problem is solved for all, as per the new wording of MED.A.030 (c):

"When exercising the privileges of a: (1) light aircraft pilot licence (LAPL), the pilot shall hold at least a valid LAPL medical certificate; (...)"

In other words, it is now "exercising the privileges" of a certain license, which governs which medical is required as a minimum, not which licence one is an "[a]pplicant" or "holder" of.

The new regulation can be downloaded here:

https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:32019R002…

Yes, that enabler, probably the more important one in general is already in law. However, in the existing Part-FCL the privileges of the LAPL are not included in the PPL (probably an unintentional omission). The change due in June corrects that.

I have information that the relevant amendments to Part-FCL passed at EASA Committee yesterday.