For such a small island, Lanzarote normally has quite an interesting cultural agenda. However, just like everywhere else, the current pandemic has shrinked it quite a bit. Nevertheless, there are still music concerts, theather plays, art galleries, and all sorts of events that should keep you entertained.
These are the main sources of information for all things cultural:
Culturalanzarote.com: this is the webpage for all events that are organised by the Cabildo de Lanzarote (main public organism of the island). Normally they have quite an interesting program of events, including theather, dance or music concerts in the different public spaces of the island.
Masscultura.com: probably the most important cultural guide/webzine of Lanzarote (in Spanish). You can filter by type of event and it has a very useful calendar where you can see all events happening in a particular day.
Coolturalanzarote.com: another online guide in Spanish, that has an English version that unfortunately is not maintained anymore.
OcioLanzarote.com: not strictly cultural, but this web hosts an updated list of markets (from handicraft to agrarian), with their current opening status and opening times/days.