A.
首先分析句子成分.
主语：That.系动词：is.表语：the writer."by whom a lot of books were written"定语从句修饰the writer.
这里的by whom 就是介词提前.相当于“whom a lot of books were written by”,由于在从句中做writeen by的宾语,故用宾格whom.
如有不懂可追问.这里的先行词是什么？the writer