Fill martini glasses with cold ice and let sit for 5 minutes to thoroughly chill glasses. Fill shaker 1/2 full with cold ice. Add Limon and shake thoroughly to chill. Dump ice from glasses and quickly strain martinis into them.
When I say "cold" ice, I mean ice straight from the freezer, not from an ice bucket. Ice from the freezer is typically around 0°F (-18°C), while ice that has been in a bucket is at 32°F (0°C). That extra coldness is very important when making martinis.
If you are in a rush, you can chill the glasses by filling them with ice and water and swirl to chill. Then empty the glasses and quickly place them in your freezer while you mix the drink in the shaker. This produces VERY cold glasses.
This island drink should NOT be served in a disposable plastic cup!