NOTE: 'Lost' indicates that the sentence is in simple past tense. 'Father' is the singular subject which requires the singular form of an auxiliary verb.
Option B - 'Were' is the plural form of the auxiliary verb used with a plural subject. As the subject in the given sentence is singular, we can't use 'were'. Hence, option A is incorrect.
Option C - 'Are' is the plural form of the verb which indicates present tense. As we need an auxiliary verb in past tense and in the singular form, we can't use 'are' here. Hence, option C is incorrect.
Option D - 'Do' is the plural form of the auxiliary verb, and it indicates the state of 'doing' something and not the state of being. Also, as it is in the present tense, we can't use 'do' here. Hence, option D is incorrect.
Option A - 'Was' is the singular form of the auxiliary verb used with a singular subject. It indicates the subject's state of being in the past tense. Hence, we can use 'was' here. Thus option A is the correct answer.
'My father's wallet was lost.'