Following the United Kingdom's agreement with the European Union on a future partnership, here are a few crucial points for travel. These are just a few basic need-to-knows, for more complex circumstances it would be wise to research for more detailed information.
Remember, Lanzarote is part of the EU by virtue of Spain's membership. The difference is there are some customs differemces for the Canary Islands. In terms of travel, there is no varaition.
Health
It appears a new document or new framework will succeed the current European Health Insurance Card (EHIC) arrangements, however the good thing is reciprocal health treatment will continue. New arrangements are described as being "akin" to those benefits the EHIC provided.
Driving
UK driving licences will continue to be valid, and therefore international driving permits will not be necessary.
Stays
There has been nothing on going further than standard third country terms for travel to the EU. This means that free movement will no longer apply to British nationals, and stays will be limited to 90 days in every 180 days (rolling period). Note that this is the whole Schengen Area, and not just one country. The clock begins on 1st January 2021, even if you are already in a Schengen country with your days prior to 1st January not being counted towards the total.
Passports
Again, there's nothing beyond the usual third country terms EU member states apply. You will need six months' validity and for the passport to have been issued under ten years ago (the EU considers passports to have expired ten years after their issue date, more here)