Lemon juice when kept refrigerated will last up to 7 days in the refrigerator from my experience.
After 7 days the lemon juice usually starts to go bad but it's best to drink the lemon juice within 2 to 4 days for the best taste and freshness.
If you want to keep lemon juice longer than a week then it's best to put the lemon juice in a freezer safe bottle such as a soda bottle or the plastic bottle the lemon juice came in and freeze it.
When you freeze the lemon juice the frozen lemon juice will last up to a 1 year before it loses it's freshness and even 2 or 3 years in the freezer the lemon juice will still be safe to drink.
But the lemon juice will not be as fresh so it's best to drink lemon juice as soon as possible.
If I want to keep lemon juice longer than 4 days I will usually just freeze it instead of refrigerating it.
During the summer we drink a lot of lemon juice and it's nice to have some frozen lemon juice that I can take out of the freezer and take on picnics or outside in our yard to drink.
The lemon juice thaws pretty quick in the summer heat and makes for a nice refreshing cold drink.