Future Press game guide description: "Provost Willem is the head of Byrgenweth, an academic institute from which the Healing Church originated. He and his students pioneered research on the old blood discovered in the subterranean labyrinths beneath the city of Yharnam, aiming to advance the evolution of humankind and achieve higher planes of thought. Despite Willem's central role in the foundation of the Healing Church and particularly the Choir, their paths ultimately diverged and Byrgenweth was abandoned by all but a few loyal scholars, now, at the end of his days and barely even able to speak, he can only sit in his favorite chair and await the arrival of one who can unlock the lake's secret."
Provost Willem was the head scholar at Byrgenwerth. Under his leadership, the Byrgenwerth scholars made their discovery of the Old Blood in the Chalice Dungeons (the 'Tombs of the Gods'). By the time the player encounters Willem he is unable to speak, and merely gestures towards the lake beside the Byrgenwerth institute.
Little to nothing is known about Willem prior to his leadership of Byrgenwerth College. It may be that he was a wealthy citizen under the Cainhurst Nobles, with his own secluded estate in the woods (later to be forbidden by the Healing Church), with an obsessive interest in archaeology and the study of history. These pursuits were evidently tailored towards the evolution of the human race, and perhaps stemmed from his impending old age, or disabilities (if he is crippled).
Willem wanted to know how to ascend beyond his current existence. The Eye Rune says that Willem was disillusioned with the limits of human intellect and wished to communicate with the Great Ones to get their knowledge/wisdom (the eldritch truth). But he was on the basest of planes, and could not communicate directly with the Great Ones who had long ago ascended to the Dreamlands and the Cosmos. His epiphany was that what he needed was more eyes, to see these Great Ones and communicate with them.
So Willem's research centred around eyes, especially adding and cultivating eyes. We can see this when the player goes to the Byrgenwerth grounds in the 'Garden of Eyes' enemies. These enemies were evidently test subjects (willing or not) for Willem who used them to cultivate eyes in their heads. Perhaps their transformation was a shock to Willem, but it likely served as confirmation that he was on the right path. We can see that the college is full of eyeballs, countless jars litter the halls which can be smashed to reveal their gruesome contents. The evidence provided suggests that what Willem was doing was taking him in the direction he wanted to go. His research allowed him to attain fragments of the “lost wisdom” of the Great Ones which can only (originally) be gained by making contact with a Great One.
Willem taught students in his college. He appears to have been a strict but respected lecturer. He pursued true knowledge, and the student uniform description indicates that he did not suffer fools. Under his tutelage were scholars like Laurence who would go on to found the Healing Church along with Micolash who would found the School of Mensis based in the Unseen Village of Yarhar'gul. Willem was also an acquaintance of Gehrman and by association Lady Maria who served Willem and Byrgenwerth as the first hunters.
Willem had an interest in archaeology and history, and this eventually led the scholars to the tombs below Yharnam carved out by the Pthumerians, who stood as watchers over the Great Ones in their slumber. Within the tombs the scholars made many valuable discoveries, the most prominent being the blood of the Great Ones. Consuming the blood of the 'gods' (“communion”) is said to be invigorating, increasing strength, stamina and vitality. It gave all the appearances of evolving mankind, exactly what Willem sought. But consumption of blood will eventually transform mankind into beasts. This truth is evidenced throughout the tombs of Yharnam and the fate of Loran. This was not the evolution Willem sought. Those afflicted with beasthood would lose their minds, becoming violent and irrational. Willem developed an adage regarding the Old Blood, drilling it into his students:
"We are born of the blood, made men by the blood, undone by the blood. Our eyes are yet to open… Fear the old blood."
Willem feared the Old Blood, and he considered any who would pursue research with the blood to be traitors. Willem's views on the Old Blood caused a schism in the school. Prominent scholars like Laurence and Micolash sought to use the blood to further their research, but Willem would have nothing to do with it. He believed that the blood, while allowing humans to reach greater levels of strength, gave the illusion of evolution and would eventually send mankind in a direction that would lead to ruin.
It would seem that prior to the students leaving Byrgenwerth the events of the Fishing Hamlet transpired. Willem is likely to have been an enfeebled old man by this point and could not have physically taken part in what happened there, but it is likely that he was the primary motivation behind the students and hunters going there. Willem sought the umbilical cord of a Great One in order to elevate his being and thoughts to those of a Great One, by lining his brain with eyes, and it is likely that Gehrman and Maria retrieved one for him by murdering the Orphan of Kos. Whatever the case, Willem managed to obtain an Umbilical Cord of a Great One, the “Cord of the Eye”. With this artefact he could further his research, taking it to new levels, higher planes.
But Willem would have to continue his research without the scholars. It is likely that Willem's research into the Cord proved that his theories were grounded and had potential, but his refusal to use blood in any way likely drove the scholars away. After the scholars left Byrgenwerth, along with the majority of Willem's servants. Willem kept back two loyal servants. He sent them into the tombs, but they both went mad. Evidently these servants were poorly equipped to deal with the dangers of the tombs, unlike Gehrman and his hunters. The fact that Willem asked his servants to go into the tombs indicates that he was still researching even after the scholars left and that he was desperate. Without anyone left to serve him, Willem was likely left aged and effectively helpless.
In his final years Willem was fond of the Lunarium Lookout and the rocking chair that he kept there for meditation. When the player encounters him in the game, he is unable to speak, but still lives. When attacked we can see that his blood is serum (https://www.youtube.com/watch?v=0RYbBxhP5rM), the blood of the Kin of the Cosmos. This blood indicates that Willem has begun a transformation into a Kin being like Rom.
With regard to Willem the Lunarium Key description notes that “In the end, it is said, he left his secret with the lake.” What the player finds in the lake is Rom, who is concealing the rituals of the School of Mensis and the presence of the paleblood moon. This indicates that Willem may have had something to do with Rom's ascendancy, and indeed the Kin Coldblood description states that “the world beyond humanity, the eldritch Truth” was “touched upon long ago at Byrgenwerth.”
Willem's influence on the events in the world of Bloodborne cannot be understated. While he ended up alone, those who would come after him would continue to follow in his footsteps. Members of the Choir; both the highest-ranking clerics of the Healing Church, and scholars would eventually continue the work that began at Byrgenwerth. Their eye covering even indicates their debt to the teachings of Master Willem, even though their paths diverged. Willem was undoubtedly a great thinker, whose ideals would have led the human race to greater planes had circumstances allowed it.