Place milk in large saucepan and stir in yogurt and lemon juice; cover and let stand at room temperature for 3 days. Mixture should be solid.
Place saucepan of solid milk mixture over medium-low heat and cook for 20 minutes. Line a large bowl with cheesecloth and pour milk mixture into prepared bowl. Lift cheesecloth to drain.
Tie filled cheesecloth around kitchen faucet and let mixture continue to drain overnight. Keep cottage cheese refrigerated in an airtight container until ready to use, up to 3 days.