Desperate people will do desperate things for the people they love. He already lost his first wife in a brutal fashion. Potentionally losing his second wife and unborn child would drive anyone to do desperate things, risks or no risks.
Now, due to him trying to save his family his daughter was taken from him. For over 3 years, he didn't know if she was alive or dead. Compounded with the ever present risk of him losing his daughter to a "mission gone wrong" scenario is an overwhelming burden to bear.
I wouldn't say that Lok offered her life "voluntarily." Sure she offered it, but it was under duress. If her father wasn't at risk of being executed, I'm sure she would have never offered her life for a random stranger. Or ask to work for the Emperor on her own.
This was a good outcome, considering the setting and time period of the story, but I'm not going to say that the man doesn't have a right to be angry just because his daughter likes working for the Emperor. His beef is totally warranted.