If the lemon juice is bottled lemon juice that you buy already made in the store then you can safely leave that out unopened.
Once you break the seal on the lemon juice bottle then it needs to be refrigerated.
But once opened you should store the lemon juice in the fridge to keep it from spoiling.
If the lemon juice is in a pitcher or homemade lemon juice then yes you have to refrigerate the unused lemon juice if you don't plan to drink the lemon juice within an hour.
Opened lemon juice can sit out for an hour but any longer than that then bacteria can begin to grow so it should be refrigerated if you're not drinking the lemon juice at the time.