Stir lemon juice into tea mixture in pitcher. In a pint glass, muddle cucumber and mint with 2 tablespoons of filtered water. Use a cocktail strainer to pour juice from muddled mixture into lemonade. Stir well. Chill for 1 hour. Serve over ice garnished with mint and sliced cucumber. Store any leftover lemonade in an airtight jar in the refrigerator for up to 1 week.