In covered skillet cook onions in cooking oil over low heat about 20 minutes or till very tender, stirring occasionally.
Remove from skillet.
Increase heat to medium.
Add liver to skillet; sprinkle with a little salt and pepper.
Cook for 3 minutes; turn liver.
Return onions to skillet.
Cook for 2 to 3 minutes longer or till liver is done.
Remove skillet from heat.
Transfer liver and onions to serving platter.
Stir lemon juice, water, Worcestershire sauce, and marjoram into pan drippings; pour over liver.
Sprinkle with parsley.