The engagement of Conrad and Lana was not cancelled despite the incident. It was because the Great Sage erased the memory of most of those who witnessed it. Only those who already knew that the sage still exist and could be trusted enough to keep it a secret knew about it the incident.
Conrad's reputation will not take a hit even if he still married Lana.
Moreover, it was hard to choose a lady to be the future Crown Prince's wife. The approval of a lot of people were needed including the current emperor, the temple, and the elders of the imperial family. The voice of the dukes and duchesses were necessary too to ensure that the future would be peaceful and cooperative.
"Please marry me. Please marry me even as your second wife. I want to be with you. I won't make the same mistake. I've learned my lesson. I swear I will do my best to support you and whoever becomes your empress," Lana sobbed and embraced Conrad.