There are many recipes out there, and I suggest you try a few and see what suits you. I like keeping both on hand, and pairing the drink to the dinner or my mood.
It all starts with the zest of your citrus of choice, in this case lemons. You can use something like 10 lemons for a full bottle, 6 for a half.
Add the zest to a bottle of Everclear, Vodka, or other neutral grain spirit. The higher the proof, the faster it will extract the citrus oils. Store the soaking mixture in a glass jar or bottle, and be careful using things like plastic funnels as very strong alcohol can mar plastics.
Let the zest soak for 4 days up to 4 weeks away from sunlight, shaking or swirling the jars occasionally.
Strain the zest using a fine mesh strainer and cheesecloth. Add simple syrup and water (if using a higher proof spirit) to taste. Store your concoction out of sunlight, possibly in your freezer. One serving option is to toss an ice cube in and have it melt to add water and chill.