Combine the water, sugar, lemon grass, ginger, and lemon juice and zest in large saucepan. Bring to a boil, stirring until the sugar dissolves. Remove from the heat and let cool.
Strain through a fine mesh sieve into a clean container and reserve for the daiquiris. (Infusion will keep for 2 weeks, refrigerated and also may be used to flavor dressings or drizzle over fresh fruit.)