Yes, the product information specifically lists eyelids as an area where this oil is well-suited, thanks to its nourishing yet easily spreading texture for skin that needs extra softness. For the under-eye area and eyelids, which have thin, sensitive skin, avocado oil's emollient properties can help improve the feel of surface dryness and make fine dehydration lines less noticeable, as described in the source.
Apply it very sparingly. Use a clean fingertip to pat a single, small drop along the orbital bone (under the eye) and on the eyelid, avoiding direct contact with the lash line where it could migrate into the eye. Gently pat until absorbed. It's best used in the evening as part of your routine. Since the skin here is reactive, always do a patch test first on your inner arm. Discontinue use immediately if you experience any redness, itching, or swelling, and avoid using it if you have a known allergy to avocados.