In a medium sauce pan add your water and sugar and bring to a boil.
Measure out 1 teaspoon of dried lavender buds
Once your sugar has melted into the water add your lavender and remove from heat.
Let the mixture come to room temperature.
Strain your mixture to remove the lavender buds and discard them.
Your lavender simple syrup is ready.
Making the drinks
Juice your lemons and strain out the pulp and any seeds with a fine mesh strainer.
Grab a cocktail shaker or mason jar and add one ice cube to the shaker, your Chartreuse, bitters, lemon, simple syrup and your egg white. This is the dry shake step.
Shake vigorously for 1 minute. You know when to stop when you hear the ice cube that you added, not shaking around anymore.
After the dry shake, you can go ahead and add ice half way up the shaker and shake again. The first shake (the dry shake) should have produced lots of foam so the second shake just helps it out more and chills the cocktail.
Pour into a martini glass and scoop out any residual egg white foam with a spoon and add to your glass.