Could you explain to this non-LAPL why that particular licence is a special case?
As hoodie says, "It isn't" but it is understandable that some should think otherwise. In the case of, for example, a PPL, the expiry date of the class or type rating is included in the licence but, in the case of the LAPL, there is no class or type rating and validity depends upon recent experience, which is only recorded in the logbook. There is no legal requirement to carry the logbook in flight but FCL.045 (c) requires that,
"A pilot or student pilot shall, without undue delay, present his/her flight time record for inspection on request by an authorised representative of the competent authority."