Rather than juicing the lemons and making simple syrup, try this CI-based approach (the lemon flavor is much fuller because some oil from the zest is included):
10-12 lemons, sliced lengthwise in half, each half sliced crosswise into 1/4-inch slices
1.25 c sugar
tiny pinch salt
optional: large handful mint leaves, or large handful strawberries or other appropriate fruit, sliced
about 5 c cold water
Place the lemon slices, sugar and salt (and optional mint or other fruit, if using) in a med-large soup pot. Mash with a potato masher till the lemon slices give up their juice, the sugar is dissolved, and the juice is thickened to a syrupy consistency, about 5 minutes. Pour half the lemon mixture and syrup through large sieve over bowl or saucepan; press on solids with masher or back of wooden spoon to release as much liquid as possible. Discard solids then transfer liquid to serving pitcher. Repeat process with remaining lemon slices (retain several mashed slices, if desired, to throw into the pitcher). Stir in water until blended; taste and adjust water if needed. Chill well and stir to blend before s