Try the Sociedad in Oasis de Nazaret
On a recent visit to Villa Antonio, I went (a few times) to the Sociedad in Oasis de Nazaret, on the main road diagonally opposite from the mini supermarket and you can see it from the balcony / terrace of Villa Antonio
People are really friendly, speak enough English to order food, drink and even a taxi !
You can find the menu via the link below
Open every day from Midday except Mondays
They were showing Champions League football on one of the visits
I tried the white wine, a little concerned when it did have a label on the bottle, however it was good, it transpired the man who works behind the bar, brews the wine at home and sells it to the local restaurants and people - If you prefer beer, a large beer is €2
Each town in Lanzarote has a Sociedad, make the effort and visit one, you will not be disappointed!