The correct answer will be women's because it is working as a possessive adjective that indicates that the locker room is the one that belongs to women, or the one in which only women can enter. As women is already the plural form of the noun, it would be incorrect to say womens to indicate the number of people. For this reason, women's is the correct option and not womens' or womens. Option A is also incorrect because it is not indicating the possessive adjective.
