——where to go,he asked a policeman. 为什么是Having lost his way and not knowing?

而不是 Having lost his way and didn't know

分词短语作状语，and 连接词属并列关系，所以这样用。

因为前边为Having，and后边的句子要和它保持一致，所以为knowing 再看看别人怎么说的。

首先,and连接的是词性相同的词，having和knowing相对。其次，having lost his way 和not knowing where to go都是独立主格，不需要完整的句子结构。但didn't know 缺少主语，且不构成独立主格。

Having lost his way and not knowing where to go, he asked a policeman. 这里Having lost his way 和not knowing where to go是两个动名词词组，他们是用and连接的同位语，因此，必须用know的动名词形式，而不能用didn't know