relations
No character in a work of fiction exists in a vacuum (unless we're talking about weird modern-art stuff here), and Walter is no exception. Much of what we learn about Walter is filtered through other characters and creatures that inhabit the castle.
characters
Listed roughly in order of importance - how useful the character is in supplying us with information about Walter.
rinaldo
Rinaldo is the number one source of information in Lament, not just on Walter, but on everything related to his castle and forest. Unfortunately for Leon, he rarely volunteers information until Leon barges in with a question about something he heard in the castle. Rinaldo's reluctance to speak makes more sense once we learn why he chooses to live so close to Walter's castle.
Five years before the start of the game, Rinaldo's daughter was turned by Walter and killed her mother and brother before fleeing into the darkness. Rinaldo was forced to create the whip of alchemy and hunt her down. He took that whip to the castle and challenged Walter, but was defeated. For some reason, Walter allowed him to live, and Rinaldo has lived in the small cabin in the forest ever since, offering help to the others who come to face the vampire.
Rinaldo is understandably skeptical of Leon's abilities, which is probably why he doesn't waste time on information until Leon has proven himself capable of defeating Walter's guardians. He starts dispensing the delicious nuggets of info once he sees Leon as a real man. :p
joachim
Oddly enough, much of what is known about Joachim and Walter isn't anywhere in the game; instead, it's hidden away in Japanese guides. From those sources, we learn that Joachim was turned by Walter, then locked away because he rebelled against his sire. We already know from Rinaldo that Walter is willing to turn humans, and this tidbit about Joachim reveals that Walter will not hesitate to punish those who defy him. Walter seems to enjoy masking his punishments as mercy; both Rinaldo and Joachim are spared their lives, but Rinaldo must go on without his family, and Joachim without his freedom.
Joachim also mentions the Ebony Stone before his fight with Leon, stating that he would have defeated Walter if not for the artifiact. After he is defeated by Leon, Joachim reluctantly shares information about the Stone's origin and power before fading away. Check the Ebony Stone section for more details.
mathias
In a way, Mathias is the most important character, as the entire plot of the game is brought about by his manipulation of Walter's desire to toy with humans. We know that he communicated with Walter at least once before the start of the game, convincing the vampire to lure Leon to the forest by capturing Sara. Mathias was counting on Leon to defeat Walter, weakening him enough for the Crimson Stone to absorb his soul.
Mathias lives on as Dracula through the power of Walter's vampire soul. It's interesting to note that Dracula's (and later, Alucard's!) signature hellfire attack originally came from Walter.
death
Death plays a small role in the story, but we are able to absorb one small tidbit about Walter from the ending scene of the game. Walter is horrified to learn that Death has betrayed him in favor of Mathias, holder of the Crimson Stone. Unfortunately, we don't know anything about Walter's relationship with Death or what benefits he gained from having Death as an ally.
succubus
To be honest, she doesn't tell the player anything directly, but only hints at the fate of Rinaldo's daughter, guiding Leon to him in search of answers.
leon
Sadly, the hero is all the way down here on the list of importance! As an outsider in Walter's world, he is unable to communicate much information about the vampire to the player. Rather, we uncover all the information that the other characters have to share through Leon's perspective. He's important to the player, but doesn't bring anything to the table in terms of original information. Sorry, Leon.