Governor-Militant Lukas Alexander
The Imperial Governer-Militant in Dark Crusade. Considered a step down in manliness from General Sturnn, Alexander is, in fact, his successor, and remains a fucking manly motherfucker, especially since Dark Crusade ends with a canon partially canon ending for the Imperial Guard (since Alexander survives Kronus, only to die on Kaurava). So whilst he does not reach the manliness of the other Imperial generals in the series, he has the standard-issue set of fist-size steel balls all guardsmen have, and he is, as such, still pretty badass. He is notable for, like all the Imperial commanders in Dawn of War, showing considerable humanity, though he is younger and less-gritty than his fellows.
He has a noted role in Love Can Bloom.
The Dark Crusade
Alexander was dispatched with his unit of the Cadian 412th in order to bring Taldeer, who was largely responsible for the manly General Sturnn's death near-death and the subsequent loss of a Dominatus-class War Titan. Having tracked her to Kronus, a planet under the rule of the Tau, Alexander commenced an orbital bombardment to clear out Tau observation garrisons before moving into the capital, reinforcing it and turning it into a formidable fortress with mazes of trenches, razor-wire, and minefields - the kind of battlefield the Tau loathe.
Shortly after landing, however, and his subsequent takeover of Ironworks Bay, the at-the-time General Alexander made a discovery with a contingent of Techpriests under his command - the main gun of an Imperator-class War Titan, cut from a Chaos Titan's arm ages ago. After Techpriests checked the cannon and found that the weapon had not been tainted by its use by the Traitor Legions, Alexander reported his findings and was given new orders: to take Kronus for the Imperium, and to salvage any relics of the Adeptus Mechanicus that may yet lie on this world. Massive support flew in, and Alexander's army swelled to gargantuan proportions, forming a spearhead that would eventually sweep all before it, doing his mentor, Sturnn, proud.
Things got complicated when Davian Thule's Blood Ravens unit arrived to purge the world and secure relics of their chapter (I.E. steal things and cover up inconvenient evidence of the Blood Ravens' hair-esy). Alexander had his orders from Segmentum Command, and wasn't about to back off because a few crimson-armored fuckwits refused to back off, despite pleading constantly that Thule was doing nothing but cause blood to be spilled needlessly. Suffice to say Thule refused to fuck off, and the Guard was forced to kick their asses and drive them off-world. Thule harbored a serious grudge. (heresy!*BLAM!*No sphess mehreen holds a grudge survives to hold a grudge against the Hammer of the Emperor!) the Guard were slaughtered in such a fantastic fashion it permanently mindfucked members of the Blood Ravens. Canon motherfuckers!
<sr>Regardless, the Imperial Guard succeeded in being the last faction standing on Kronus (apart from the Blood Ravens in North Vandea), and with that, they had won. The Adeptus Mechanicus began to salvage the Titan's gun and work on restoring the world for the Imperial citizenry, several prominent captains and sergeants got promoted for their valor, and the Governer-Militant had a new planet to lord over. Taldeer had also been brought to justice - the Blood Ravens had beaten him to the punch, and finished off the Eldar in their stronghold. For the Governer-Militant, it seemed like things were only on the up-and-up, and little could stop his meteoric rise in power... except for the Kaurava Campaign. Hahaha. No.
The Death of the Governor-Militant
Shit hit the fan when the 1st Kronus Regiment was sent to assist the 252nd Kauravan in securing their system, which had recently been overrun with aliens and heretics. Unfortunately for the Liberators, problems arose immediately - Tau forces of the Fal'shia Sept had moved into the system and were reinforced heavily, putting up intense resistance. The men of the 1st Kronus Regiment suffered crippling casualties, including Colonel Bosch, whom the Governor-Militant had placed in forward command. Wondering what the hell was going on and why a bunch of aliens had just managed to waylay Alexander's forces, he moved in and proceeded to make a landing on one of the planets in the Kauravan system with a sizable contingent of his forces.
It was a massacre. The Tau had been laying in wait, and ambushed his forces with overpowering force, cutting the Guardsmen down piecemeal. In spite of this, Alexander kept his cool, and directed his forces forward, inflicting enormous casualties on the alien space commies. Sadly, he then took a Fusion Cannon blast from the Tau Commander to the torso, burning a hole right through his chest (and armor), before the Sisters of Battle arrived to deal with the Tau. As a note, the sisters did not finish off the 1st Kronus Regiment soldiers, as they too are from out-of-system and from a now-loyal Imperial world (marking them as one of the few things "clean" in the Kauravan system in their eyes).
TL;DR: He dies in the intro of Dawn of War Soulstorm's intro, trying to help the 252nd Conservator Regiment (under Vance Motherfucking Stubbs) retake Kaurava. It sucks because it's a completely unceremonious death for someone who accomplished as much as he did. It's worth noting however, that the chain of Grit continued - Sturnn's death near-death led to the rise of Alexander, whose death, in turn, led to the rise of Stubbs.
His death encouraged Stubbs to get his shit into the game, encouraging the 252nd Kauravan towards greater acts of bravery and valor, and eventually allowing Stubbs to emerge triumphant in the Kaurava Crusade.