新概念英语2第18课的第一句是否有问题?

是After I had had lunch at a village pub,I lookde for my bag.这句话吗?have lunch是一个动宾结构,表示“吃午饭”,have本身是个助动词,但在have lunch 这个词组中是完全动词,也就是表示“吃”.这是第二个have.
第一个have是助动词,作为助动词可以构成各种时态.根据全文,这是一个过去完成时,所以是I had had lunch.
只能讲到这样,加油!