首先,非谓语动词没错,看来也没啥问题
其次,如果两个或几个动作连续发生且衔接紧密时用一连串的一般过去式即可
如：He locked the door and went away.
Mr.Smith went to the market,bought some flowers and went to see his friends.
用了Having lit就太别扭了,除非有上下文特意交代暗示.而答案最符合日常语言习惯