In a saucepan, combine the lemon juice, honey, lavender and 1/2 cup water. Bring to a boil, then turn off the heat and let steep for 30 minutes. Pour through a strainer to remove the lavender.
Add the remaining 1 1/2 cups cold water to the strained lemon juice mixture, then pour the liquid into your popsicle molds.
Freeze for 2 hours, or until the popsicles are slushy enough that you can insert the popsicle sticks. Freeze overnight, or until solid.
To remove from the mold, run a little warm water over the molds for a few seconds, then gently wiggle the popsicles free.
Wrap each popsicle individually in wax paper, and store in a freezer bag or airtight container.