Add basil, garlic, Parmesan, pine nuts, and lemon juice to a food processor. Pulse a few times.
While the processor is running, slowly stream in the olive oil. If your processor does not allow for this you can add the olive oil in a couple batches, pulsing well in between.
Add salt and pepper to taste.
Use right away or store in an air tight container in the refrigerator for at least 5-7 days.
Notes
If you don't have fresh lemon you can substitute lime juice or apple cider vinegar. This will change the final flavor but still works well.