Fresh lemon juice should keep it's fresh taste for as long as two weeks in the refrigerator.
Fresh lemon juice will still be okay and safe to drink after two weeks in the refrigerator although it will start to taste bitter and less tangy and less bright and once again there's nothing wrong with drinking it after the two weeks so you don't have to throw it out it will just not taste as good or fresh as it did after the 2 weeks.