Many people misunderstand the differences between lactose free formula, cow's milk based formula, and soy formula. While lactose free formula and soy formula both do not contain lactose, lactose free formula is created from cow's milk and thus contains cow's milk protein.
Lactose free formulas are refined to remove the lactose and replace it with a different carbohydrate. Because it contains cow's milk protein, lactose free formulas do not work for babies who are truly allergic to milk. Rather, it can be an alternative for babies who are lactose intolerant.
Lactose intolerance, however, is more commmon in children after they have turned age 2, so lactose free formula is not commonly used.
This type of formula can come ready-made or in powder that you would need to mix with water. See also: Water Guidelines for Baby Formula.
What about generics, DHA, and the like? For more info see: