Combine 1 cup water and sugar in a small saucepan. Rub torn verbena to bruise; add to pan. Bring sugar mixture to a boil, stirring gently as needed to dissolve sugar evenly; cook 30 seconds. Remove from heat; cool completely. Strain mixture through a sieve over a bowl; discard solids.

Combine sugar mixture, gin, soda, and juice. Serve over ice. Garnish with verbena sprigs and lime slices, if desired.