His Astra Militarum forces landed in an abandoned city, and found traces of ancient relics scattered across the planet, including a "Hellstorm Cannon", a piece of weaponry from a Horus Heresy-era Imperator-class Titan.
The city was renamed "Victory Bay", and Tech-priests began excavating the massive Hellstorm Cannon. The Imperium gave Lukas Alexander the title of "Governor-Militant" of Kronus, and tasked him with conquering the planet for the Imperium.
Alexander formed the 1st Kronus Regiment of the Astra Militarum, which he named "The Liberators," since he believed his soldiers were fighting to free the humans who were on the planet. Unfortunately, his goals put him at odds with a Blood Ravens force who came to Kronus trying to uncover mysteries about their Chapter's past.
The Blood Ravens had been ordered to purge the planet in order to ensure the secrecy of their findings. They warned Alexander to leave, but he was determined to follow through with his orders and push the other factions off Kronus.
If the Governor-Militant was successful in his task, he would become one of the most powerful men in the galaxy with an entire planet at his command, loyal Guardsmen, a Hellstorm Cannon, and a debt owed by the Tech-priests of the Adeptus Mechanicus. He would also, however, have gained an enemy in the form of the Blood Ravens, who will probably be too busy defending themselves in front of the Inquisition to bother with him.
When Alexander's Imperial Guard troops finished off the other seven races in Dark Crusade, most of the 1st Kronus Regiment is sent off-world to other battlefields while Lukas Alexander stayed behind to oversee the creation of a new government and train the new Kronus Planetary Defence Force. The Adeptus Mechanicus is grateful to Alexander for defending them while they completed their study of the Hellstorm Cannon.
The human population that had chafed so long under T'au control rose up and murdered every single T'au once Alexander destroyed the T'au stronghold. His men seized documents from the Blood Ravens' razed Castellum Incorruptus in North Vandea that showed previous visits to the planet and shocking gaps and contradictions in the Chapter's history -- which called into question the true origin of the Blood Ravens.
After Alexander destroyed the Webway gates that transported the Aeldari forces back and forth from their hidden starship in the sector, he told his men that even though they had finally captured the Farseer Taldeer, they now had to focus on defending the freedom of the people of Kronus. The Farseer was then handed over to the tender mercies of the Inquisition.
Lukas Alexander is as much a politician as a soldier. A skilled speech-giver and master of rhetoric, he is both imposing and charismatic. However, he allows his Commissar, Anton Gebbet, to do most of his dirty work for him.