Prufrock was going to:

visit a lady friend

have an affair

go to a funeral

go to the library

both a and b

The answer is : Both a and b

In the Love Song of J. Alfred Prufrock, he write the poem to address his wife.

In the poem, he wrote about another woman and there's a sentence that said "settling a pillow by her head" which is very likely mean that the lady is his mistress"