Save your money at home, book a return flight (with return date a month after you land), print out a CV with your picture on the back, buy comfortable shoes and then start pounding the streets from bar to bar and restaurant to restaurant. Call back a week later and ask again if there's any work going. Repeat the process until a few days before your return flight.
Things are not like they were years ago, but there is still work to be found if you're lucky.
You don't need residencia to stay here for a month and look for work during that time. The pay rate is correctly quoted by lanzalocal, and you will have to work long hours too.
But if you're 19 and have no commitments, then Lanzarote can be a great place to live.
BTW, I'm based in Puerto del Carmen, and I've been made aware of 3 different bar/restaurant jobs in the last week. They're probably gone now, but there's no question that jobs do crop up.
I will now assume the crash position and await the rebuttals from other posters