Using a vegetable peeler, remove the peels from all the lemons. Only remove the outer yellow layer as the white pith tends to be bitter. Transfer the peels to a large jar and cover with vodka. Cover with a lid and allow the mixture to infuse for anywhere from one to four weeks in a cool, dry place away from direct sunlight. The longer the mixture infuses the more lemon flavor your cocktail will have.
Line a strainer with a cheesecloth or a large coffee filter, set it over a large measuring cup (6 cups or more) or bowl. Strain the infused vodka.
Combine two cups of sugar with two cups of water in a medium pan. Bring the water to a simmer and stir until the sugar dissolves. Remove from heat, add in the lavender (if using) and allow to steep of 30 minutes. Strain the syrup into the infused vodka and stir to combine.
Store in a large jar or several small bottles in the refrigerator.
