Make syrup: In a small pan, bring honey and water to a low boil, then add the lavender. Remove from heat. Let steep for 30 minutes, then strain.
Make shrub: Add all ingredients together and shake, then strain into a coupe or martini glass.
*Seedlip is the world’s first nonalcoholic spirit. Produced in London, it tastes similar to gin and is available stateside at select Whole Foods Markets and boutique liquor shops.