Place avocados, cilantro, lemon juice, salt, onion powder, and white pepper in a blender jar or food processor bowl. Add chicken broth; cover and blend or process until smooth. Transfer to a glass bowl. Stir in milk, cream or sour cream. Cover and refrigerate for at least 3 hours or up to 8 hours.
Stir before serving. Season to taste with additional salt and white pepper. If necessary, stir in more milk to reach desired consistency. Garnish with lemon slices, if desired.