In a cocktail shaker, muddle together strawberries, basil, lemon zest, and sugar. Use the back end of a wooden cooking spoon if you don't have a muddler.
Add in vodka and lemonade to the cocktail shaker.
Close tightly and shake for a good minute or two.
Pour into cocktail glasses over ice.
Garnish as desired.
Notes
Using a cocktail shaker strainer might make this drink a bit pulpy. Add a fine mesh strainer to strain out more pulp if you prefer it this way. Me? I'll drink it any way it's served. Bottom's up!