
It is briefly explained in ch. 66 when the duke left the clematis brooch in lius‘ quarter when heading off to war and then again in ch. 68 when lius and his brother visit the military camp. The ihar coat of arms (the dukes family symbol) is made up of an eagle which represents the head of the dukedom and the clematis flower which represents his spouse/ his other half. So the clematis brooch is an heirloom gifted to the better half/ Duchess of the duke, ruler of the north. So by asking camellia to be his clematis, he asks her to be his wife. In other words to complete the dukedom as represented on their flag.
I'm still wondering and searching for what "be my clematis" mean. let me know please.