While I believe you are correct that the UK CAA will recognise foreign EASA licences until at least end 2023, they have also stated that any UK issued EASA licences will automatically become UK national licences on 1st Jan 2021. So if you have a LAPL today then it will continue for the foreseeable future, with the same revalidation/currency requirements.
However EASA have not said they would recognise UK licences after end 2020. Those with UK PPL licences, which are at the internationally recognised ICAO level, will be able to use them abroad. However since the LAPL licence is sub-ICAO, it wouldn't be.
Of course, many things may change between now and 1st January, but as it stands, UK LAPL holders won't be able to use their licence abroad. You would have to upgrade to a full PPL.