Hi Norman. Assuming you are a British citizen, and you want to relocate here, you now need to apply for a visa prior to arrival on the island: https://lanzaroteinformation.co.uk/lanzarote-visa-information/
On property rentals, do you use Facebook? If so, there are several groups there, just search Facebook for “Long term rentals” Lanzarote and you should find them. Another option is too check websites like this one: https://www.idealista.com/en/alquiler-viviendas/las-palmas/lanzarote/