Combine water, honey, thyme and ginger in a medium saucepan. Bring to a boil over medium-high heat. Reduce heat to maintain a simmer and cook for 5 minutes. Remove from heat; stir in lemon zest and lemon juice. Let steep for 20 minutes.

Strain the mixture through a fine-mesh sieve into a medium bowl. (Discard the solids.) Refrigerate until cold, about 2 hours or up to 5 days.

To make each drink, combine 1/4 cup of the lemon mixture with 1/2 cup sparkling (or still) water and 1 ounce gin (or vodka), if desired. Garnish with a thyme sprig, if desired.