Agree with what MJ has said above but:
FCL.135.A LAPL(A)
(a) The privileges of an LAPL(A) shall be limited to the class and variant of aeroplanes or TMG in which the skill test was taken. This limitation may be removed when the pilot has completed in another class the requirements below:
They would need to take an LAPL Skill Test otherwise there is no aircraft in which they would be entitled to exercise the privileges.
FCL.140.A LAPL(A) — Recency requirements
(a) Holders of an LAPL(A) shall only exercise the privileges of their licence when they have completed, in the last 24 months, as pilots of aeroplanes or TMG:
(1) at least 12 hours of flight time as PIC, including 12 take-offs and landings; and
(2) refresher training of at least 1 hour of total flight time with an instructor.
Holders of an EASA ATPL or CPL are not holders of an LAPL. They have other Licences (which contain LAPL Privileges). Therefore, it would seem, according to Part-FCL, that the LAPL Recency Requirements do not apply to ATPL or CPL Licence holders.