1. Put 18 cups milk and 2½ tbsp. salt into a large pot; bring just to a boil, stirring occasionally.
2. Add ½ cup fresh lemon juice; turn off heat. Large curds will form. Using a wooden spoon, gently push curds together toward one side of the pot; do not stir, or the curd will break into small pieces.
3. Strain mixture through a colander lined with 4 large layers of dampened cheesecloth. Let curds drain briefly, undisturbed.
4. Gather ends of cheesecloth together to form a purse. Tie ends around a wooden spoon. Place spoon over a large pot, balancing ends so that purse hangs freely. Let drain at room temperature for 1 hour. Discard any liquid that collects in pot.
5. Unfold cheesecloth and rewrap curds into a rectangle; wrap package in a kitchen towel. Place package on a cutting board and top with a baking sheet; weight down with several heavy pots and pans. Press cheese for 1½ hours, rewrapping and tightening the cheesecloth every 30 minutes (which helps form a compact shape).