Zest the lemons with a microplaner, being careful to avoid the white pith as much as possible. Discard lemons (I make lemonade with them).
Place vodka and lemon zest in large jar. Let steep for a week, shaking occasionally. Add sugar. Let steep for another week, shaking occasionally, or until the sugar is all dissolved. Strain and bottle. Allow it to sit for a couple of weeks for the flavors to marry (the longer the better).
(You can use a paring knife to zest the lemons into strips instead; this makes straining easier, but you need to steep it longer to get full extraction.)