Here is some of the Plot from the Diablo Wiki describing the cathedral and monastery.
The setting of Diablo includes the world of Sanctuary, as well as
Heaven and Hell. After eons of war between angels and demons, the
ascension of man prompted the three Lords of Hell (including Diablo
himself) to seek victory through influence, prompting their exile into
the mortal realm. There, they sowed chaos, distrust, and hatred among
the humans of Sanctuary until a group of magi trapped them in
soulstones. Diablo's soulstone was buried deep in the earth and a
monastery was built over the site.
Generations passed and the purpose of the monastery was forgotten. A
small town named Tristram sprang up next to the monastery's ruins.
When King Leoric rebuilt the monastery as a cathedral, Diablo
manipulated its archbishop to destroy his soulstone prison. Diablo
subsequently possessed the king, sending out his knights and priests
to battle against peaceful kingdoms, and then possessed the king's
son, filling the caves and catacombs beneath the cathedral with
creatures formed from the young boy's nightmares.
Tristram became a town of fear and horror, where people were abducted
in the night. With no king, no law, and no army left to defend them,
many villagers fled.
Small timeline (taken from here):
- 1262: King Leoric and Archbishop Lazarus come to the town and remake
the old monastery into a Zakarum church.
- 1263: The events of Diablo I.
- 1264: The rogues of the Sisterhood of the Sightless Eye are forced
out of their monastery and corrupted by Andariel, who is subsequently
slain.
One more regarding the Cathedral itself, and the Religion:
Tristram's Cathedral is an ancient Horadrim edifice. Under it, they
imprisoned Diablo in his soulstone. When the Horadrim faded away, the
cathedral is left as decrepit ruin. When the Zakarum came to be the
most practiced religion, the Cathedral became a place of worship and
the seat of King Leoric, who converted Khanduras to the Zakarum
religion.
To summarize it: The monastery was 'dedicated' to keep Diablo in his prison.
King Leoric rebuilt the monastery into the cathedral, and Diablo manipulated the archbishop to release him from his prison. The capital of Khanduras, Tristram, took Zakarum as a religion.
Other sources: http://www.diablowiki.com/Archbishop_Lazarus_%28Diablo_I%29