Put the lemon peels, lavender, if using, and rum or vodka in a container and let stand for 4 weeks.
Strain the mixture into a decanter.
Mix the sugar and water in a medium saucepan and bring to a boil. Reduce the heat and simmer until the sugar has dissolved. Let cool before adding to the rum mixture.
Serve in small aperitif glasses.
Store in the freezer for up to 1 year.