lucky enough to have many people-----him with the work this

我也认为应该选择A
have sb.do sth:使某人做谋事
have + sb （宾语） + do sth （宾语补足语）意为“让 / 叫 / 使某人做某事.
此结构中的 have 是使役动词,sb 作宾语,其后的 do sth 是省去 to 的动词不定式作宾语补足语.例如：
The boss often has them work for 14 hours a day.
老板经常要他们一天工作 14 个小时.
I'll have someone repair the bike for you.
我会让人为你修理自行车的.