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.
