The correct option is B by herself
Intensive pronounces end in either –self (if it is singular) or –selves (if it is plural). They are myself, ourselves, herself, himself, itself, themselves, yourself, and yourselves. We can use these pronouns to add emphasis to a sentence. Here emphasis is added to the fact that the old lady, in third person, lives all alone, that is, herself. A preposition "by" is introduced to explain the relation between the verb and the pronoun, that is between "living" and "herself". Hence, Option B is correct. The rest of the options do not adhere to this rule, hence incorrect.