Wash and dry the lemons, then halve lengthwise and cut into slices between 1/4" and 1/2". Put the slices in a heavy-bottomed medium-sized pot or saucepan. Add good olive oil (it doesn't have to be extra virgin) to cover the lemon slices.

Heat the mixture under the lowest possible heat for one hour. You're looking for a slow simmer — the occasional lazy bubble — but want to avoid a full simmer.

When time's up, remove the pot from the heat. As soon as the mixture is cool, seal in jars, label with the date, and store in the refrigerator for up to 2 weeks or in the freezer for up to 6 months.