It may be that the reason that Baritt refused to countenance the assassination of Aliera e'Kieron (and her cousin Morrolan) was because he had strong romantic feelings for her. Aliera may have been aware of these feelings, although we don't know if she reciprocated them. She does seem to have felt a least a certain amount of sympathy for Baritt, though.
Alternatively, Baritt may have simply felt strongly loyal to Adron e'Kieron, and was reluctant to permit the murder of that man's daughter.
To the left, Dragonlords in general hold assassination in contempt, preferring either duelling or outright war as the only honorable ways to kill an enemy. Baritt was certainly a proud Dragonlord and could simply have been unwilling to countenance assassination of any kind.
Morrolan tells Vlad that it was Aliera's right and duty to give the benediction at Baritt's funeral. Vlad later figured out why Aliera had that right and duty, but he refused to reveal it to his readers, although he implies that it was a matter of the internal politics of the House of Dragon. This "duty" might simply have been a result of the fact that Aliera was the Dragon Heir at the time, and as such, she was the most fitting individual to convey the respects and honors of the entire House to the deceased.
Another possibility, which would be consistent with Aliera having the "right and duty" to honor Baritt rather than for any of his descendants to do so, is that perhaps Aliera had been officially betrothed to Baritt, rather than his lover. If this had been a formal alliance between two very high-ranking Dragonlords, rather than a love-match, it might explain Aliera's muted and perhaps somewhat conflicted feelings towards him.
It is interesting to consider how Pathfinder, held for many years by Baritt, and apparently destined to be held by Aliera, may have been involved in whatever relationship the two may have had.
Pathfinder saved Aliera even from a blow from a Morganti blade; it is curious that the Great Weapon did not act in a similar fashion to save Baritt when he was assassinated. Perhaps he had forgotten it in a drawer at the time. It is not known if Baritt even ever realized Pathfinder's true nature, or if it had ever "bonded" with him, although Vlad seemed to believe that Baritt had concealed Pathfinder within the nondescript (for a Morganti) Greatsword.
To the left, Morrolan tells Vlad in Dragon that Baritt was "too good." This implies that Baritt used Pathfinder to help him achieve all of his amazing feats. Obviously, if Baritt used Pathfinder, he knew he had it. Also, how did Fornia know Baritt had Pathfinder? And how did Fornia know that Pathfinder was concealed within the Greatsword? If even Baritt did not know what he had, how could Fornia even possibly have any chance to know?