Drain the lemons and let them cool until you can handle them. Cut them open and remove the seeds, but keep everything else. Do this on a plate so you can retain all the juices. Once you have removed all the seeds, put everything into a food processor. Process until finely pureed. You may need to pulse the machine at first, and scrape down the sides as necessary to get everything smooth. This will only take a couple of minutes. You will need one cup of lemon puree for the cake.