Almost all of the UK or Irish bars in Spain have wall to wall sport on all day.
You shouldnt have a problem finding a pub finding the horse racing on
I was in Puerto Rico in Gran canaria 2-3 years back when the festival was on, there was a bookmakers in the shopping complex and one pub i was in had the racing on .Cant remember the name of the pub though.
I would say that 99% of Irish Bars in Puerto del Carmen Lanzarote that are open during the day will be showing racing,check the black boards outside the Pubs. The Drop Inn on Calle Anzeulo has a Bookmaker on site to take bets. I will be there myself during Cheltenham, Paddys Day, Easter
Loads of bars in Puerto del Carmen show the racing every day. Many of them have their bookies on site. I always watch it is the Palms bar on the main strip.