Thinly slice the lemons and toss them with sugar in a bowl. Transfer the lemon sugar mixture to a glass jar, seal it and let sit for 3 days on the counter. Roll the jar whenever you think of it.
After 3 days, add the lemon/sugar mixture to a sauce pan and bring to a simmer to dissolve the sugar. Strain the solids out using a cheesecloth.
Add strained syrup to a clean pint bottle or jar. You can top off with clean water, but this may thin the syrup out too much. You want a nice bitter bite to go along with the sweetness. If you want a thicker, stronger syrup, skip the water.
Fortify with rum to preserve (if you think necessary). Store in the fridge.
Makes about 1 pint of syrup.
If you have normal lemons and want to remove the wax, soak them in a solution of 1 quart of water and 1 oz of white vinegar for one minute. Then rinse with cold water and scrub dry with a paper towel.
Be sure to sanitize the implements you will be using. I have had better luck using the vinegar solution on normal lemons - this might be "sanitizing" the fruit.
If you leave a bunch of juice on your counter/cutting board as a result of the slicing, you can make up for this by squeezing 1/3 of a lemon in the lemon sugar mixture.