The ducts of the lacrimal gland open into the:

Lacrimal Fluid is produced by the lacrimal gland, which lies in a fossa in the superolateral pa of each orbit. The fluid from this gland enters the conjunctival sac through up to 12 lacrimal ducts that open into the superior conjunctival fornix. The tears then flow to the medial angle of the eye and collect in the lacrimal lake. The lacrimal papilla are small elevations on the eyelids, found near the lacrimal lake. These papillae have small opening called the lacrimal puncta; tears flow from the lacrimal lake into these puncta. From there, the lacrimal fluid goes into small canaliculi which drain the fluid into the lacrimal sac. The lacrimal sac continues on as the nasolacrimal duct and drains tears into the inferior nasal meatus. Ref: Moon D.A., Foreman K.B., Albeine K.H. (2011). Chapter 18. Orbit. In D.A. Moon, K.B. Foreman, K.H. Albeine (Eds), The Big Picture: Gross Anatomy.