In a pitcher (at least 2-qt. capacity), stir lime juice and 1/4 cup honey until blended. Taste; if mixture is too tart, add up to 1/4 cup more honey. Add 5 cups water. Chill until cold, at least 1 hour, or up to 1 day.
Just before serving, add ice cubes. Thinly slice lime crosswise (discard ends), cut slices in half, and add to pitcher.