Lazarus had been exposed to Mephisto's Soulstone at some point prior to arriving in Tristram. He was initially corrupted by the Lord of Hatred before being sent to Tristram as representative of the faith of Zakarum. While serving King Leoric, Lazarus encountered Diablo's soulstone beneath the Tristram Cathedral and was compelled to free Diablo.
The how and why of the corruption is moot. The Prime Evils had discovered degrees of latitude while being imprisoned within their soulstones; they could only influence individuals physically close to them, but that influence could be very strong.
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Be it through hallowed grounds or lands of sorrow
All in the Forger's wake is left bereft and fallow
Is the residuum worth the cost of destruction and maiming;
Or is the shaping a culling and exercise in taming?
The road's goal is the dark Origin of Being
But be wary through what thickets it winds.
-Excerpt from the Litany of Residuum;
As Translated by He Who Brings Order