The representative of Lu clan was force leaving with empty-handed, they never have though Zhao Li Xin would continue the war moreover it's only for one woman they convince his action is only on a fit of anger after several days they think Zhao Li Xin would come down and didn't pursue the matter farther, no sane man wants to get involved in unfavorable war.
Then the Lu clan take, they're presumptuous imagination to another level, Lu clan is one of the most powerful families in the northern region they're position even match the northern royal family so they slightly underestimated Zhao Li Xin despite all the rumor about him.
They want to show to other people that Lu clan is the power that no one can trifle not even Hei Shen so they acted magnanimously to give a chance for Zhao Li Xin to explain his behavior for killing one of the Lu clan and for a reward they would granted Hei Shen with forgiveness.