Melissa Shelton, DVM offers the following formula. We would not use essential oils because essential oils don't blend well with water. Consider using Lavender hydrosol instead for a safe and effective alternative.
Lavender Eye Spritzer
4 oz distilled water
Glass spray bottle. Shake well, mist into eyes or surrounding eye tissues.
Spritz into the eye 4 or more times daily. Some have used this daily for 2 months without harm.
Don't aggressively attempt to spray into the eye; the goal is to lightly mist the area, and if possible hold the eye open slightly while doing so.
from the Animal Desk Reference by Melissa Shelton, DVM, page 51