If you prefer a milder flavor, use ripe black olives instead of green olives. Liquid egg product is available in cartons in the freezer or refrigerator section of most supermarkets.
Combine pitted green olives, egg product, lemon juice, and seasonings in the work bowl of a food processor or blender. Process until the olives are chopped to a purée; scrape down the sides of the bowl with a rubber spatula.
With the machine running, pour olive oil into the work bowl in a thin, continuous stream. If necessary, stop the motor and clean the side of the bowl once again so that all of the purée is incorporated.