What are the rules for this grammatical construction: 我去听他的演讲去晚了
Two clauses compressed to one by reintroducing the verb. The first instance is descriptive (I am going to listen to his lecture). The second instance describes the result of the action (I came late).

You need to reintroduce the verb to give 晚 the proper context. Without it, 晚 would refer to 演讲.

Sometimes you can omit one instance of the verb: 你（说）汉语说得很流利。

Sometimes you really have no choice: 你说汉语比我说汉语说得好。