Maybe. Some people, such as those with restrictive diets (for example, diets that limit the number of calories per day and vegetarian diets), may not get adequate nutrients through their diet alone and may be at greater risk for nutritional deficiencies.
In addition, the recommended dietary allowances (RDAs) (the average amount of a vitamin or mineral that meets the daily nutrient needs of nearly all healthy people) for some nutrients (such as iodine) increase while breastfeeding; therefore, it is possible that diet alone may not be sufficient to ensure adequate nutrition for women who are breastfeeding.
In these cases, breastfeeding mothers may benefit from taking a multivitamin supplement.
Source: CDC