Cut lime in half. Slice one half into quarters; add quarters to strawberry mixture. Squeeze juice of other lime half into strawberry mixture; discard squeezed lime.
With a wooden spoon, muddle strawberry mixture until well blended and sugar has dissolved.
Add gin to glass; cover glass and shake well for 30 seconds.
Pour strawberry mixture through a strainer evenly into 2 glasses. Add ice to each glass; top each glass with 1/4 cup soda water.