Puree strawberries and send them through a fine sieve to catch the seeds. Whisk in cool lavender simple syrup and lemon juice. Taste for balance of acid and sweetness. Chill overnight in freezer.
Lavender Simple Syrup:
Combine the sugar and the water in a saucepan. Bring to a simmer and cook until the sugar has dissolved. Remove from the heat and cool. Bring simple syrup back to a simmer and toss in dried lavender. Cover and infuse for a 30 minutes. Strain and cool. Store in a refrigerator.