In the sentence “He described the picture as expressing the dream of mankind,” the phrase “as expressing the dream of mankind” is an adverbial complement to the sentence. It is an added expression by which the predication of that sentence is made complete.
Here’s a suggested construction combining all of those three sentences of yours in just one easy-to-understand sentence:
“She quoted Lu Xun as saying that the picture expressed the dream of mankind, showing that the painter had learned his lessons well.”
This construction assumes that Lu Xun isn’t the painter referred to and that the painter is male.