This question is about the posterior thorax and the thoracic outlet
What lies anteriorly to the sympathetic trunk on the left?
The thoracic duct.
The thoracic duct lies in front of the vertebrae on the left and drains all of the lymph below the diaphragm from the cisterna chyli, and usually the left half of the thorax via the left jugular, subclavian and mediastinal lymph trunks. It drains into the left brachiocephalic vein.
The right thoracic lymphatic vessels tend to open up into the right brachiochephalic vein independently.
The thoracic duct passes through the diaphragm with the aorta at T12.