The Foreign & Commonwealth Office website links to the official Canary Islands Tourist Board website, which largely answers your question:
https://www.hellocanaryislands.com/travelling-to-the-canary-islands/
You'll see that (unless you've got proof of having had Covid-19 and recovery from it), you require EITHER proof of a negative NAAT test (which, in practice, means a PCR one) OR proof of full vaccination.
The FCO website states:
"Spain will accept the UK’s solutions to demonstrate your COVID vaccination status".
https://www.gov.uk/foreign-travel-advice/spain/entry-requirements
Therefore the Spanish authorities (in Lanzarote) WILL accept your UK proof of vaccination (via the NHS app on your phone or in printed form) for entry and you do NOT require a PCR test to visit the Canary Islands.