Combine water and horehound in a large saucepan. Bring to a boil. Reduce heat; simmer 30 minutes. Remove from heat; cover and steep 30 minutes. Strain; discard horehound, reserving liquid.
Combine liquid, sugar, and cream of tartar in a medium saucepan. Slowly bring to a boil, stirring until sugar dissolves. Cover and cook over medium heat 2 to 3 minutes to wash down sugar crystals from sides of pan. Uncover and cook, without stirring, until mixture reaches 220°; add butter (do not stir). Continue cooking, without stirring, until mixture reaches hard crack stage (300°). Add lemon juice (do not stir). Gently shake pan.
Quickly pour syrup into a buttered 15- x 10- x 1-inch jellyroll pan. Let cool slightly. Mark top of warm candy into 1-inch squares, using a sharp knife. Cool completely; break into squares. Wrap each square in waxed paper.