How long can a bottle of self-made basil sauce last without rotting?
Last summer was a long time ago. The National Center for Food Preservation has this to say about herbs in oil: 


  Oils may be flavored with herbs if they are made up for fresh use, stored in the refrigerator and used within 2 to 3 days. There are no canning recommendations. ... Pesto is an uncooked seasoning mixture of herbs, usually including fresh basil, and some oil. It may be frozen for long term storage


Clostridium botulinum is a serious enough hazard with oiled herbs that I'd not trust a dash of lemon juice on top of the oil to protect me from getting sick after 9 months storage. You're much safer freezing the stuff as recommended.  Ice cube trays produce nice pesto cubes that you can store safely in a freezer bag for at least a couple years.