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Here is Some lore of one of my Homebrew Astra Militarum Regiments as found on the Homebrew 40k Wiki. I am TechCaptain there so this is mine.

No finer cavalry are found around the Ishtar Subsector than the Lunar Venatorii Cavalry Regiments and their Wyrm Riders. They are the best the Astra Militarum of Ishtar has to offer, and they form the breakwater defense needed to continue Imperial interests. On the training moon of Verliaus, the academies of war train the best and brightest of the Fringe if not the sector. Heavily fortified' with every terrain available for training, the programs of Verliaus know no bounds. Veralius has come to be a renowned academic world, where scholars, specialists, and soldiers from across the sub-sector go to study, and it is also home to numerous Schola Progenium facilities. It is here among the populace of the training moon that the elite regiments of the Lunar Venatorii are raised, equipped with the finest of gear and trained at the finest of academies. The Regiment's officers even travel downwards to Tarakon and engage in the sacred ritual of wyrm-bonding, earning their right to command regiments of Venatorii and becoming honorary members of House Fásacha. Indeed it is the Venatorii that often accompany the Knights of House Fásacha in battle to deal with the most dire threats to the frontier, as well as fighting the bloody battles of expansion.

Orbiting Tarakon is the Civilized Moon of Veralius, whose surface is studded with the many edifices and colleges concerning the academia of war. The people of Veralius have long been tied to Tarakon for which they orbit, and they too have taken upon many aspects of the Wyrm. They have sought to embody its natural keen intellect and wisdom, as well as its merciless ability to slay all those who offend its honor. To this end, Veralius has long been a source of additional warriors for House Fáscha, separate from the House and its traditions, but highly valued nevertheless as cunning scouts and keen warriors with which to defend against the dark predators slinking form the void. With the arrival of the Imperium, Veralius built across its landscape renowned colleges and institutions of war, its peoples immersing themselves in the arts of battle and the warrior ethos of the Wyrm. The Adminsitratum quickly built Schola Facilities up from these war colleges, again separate from the peoples of Tarakon, but drawing upon their hard-earned wisdom. Soon Veralius became a major School facility in the region, producing many fine officers, beauracrats, sororities, commissars, and storm troopers gathered from the orphaned scions of the Imperium. Yet still the Veralius war colleges produced their own soldiers with their own proud lineage and killing edge. These warriors became known as the Veralian Lunar Venatorii. Each a warrior-born, trained from childhood by the warrior colleges, with the ethos of the Wyrm and a love for the Emperor becoming their creed.

The Venatorii excel at raiding and skirmishing, and are used by the Imperial Guard as guerrilla fighters to great effect all across the galaxy. A squad of skilled mounted cavalry can be used as an effective assault and skirmishing force, able to move rapidly over the broken ground. They can then act in the roles of scouts, patrols and fast response troops. Lunar Venatorii are also used to operate out on their own beyond the reach of normal lines of communication, deep within enemy territory. This enables them to harass enemy troop movements by using guerrilla tactics. They specialise in using terrain features and light cover to hide their movements, appearing suddenly over a rise or from behind a ridge and riding quickly down on their enemies.

The Lunar Venatorii make use of standard Astra Militarum equipment. All Lunar Venatorii are issued Venatorii Carapace Battle Dress and Mjorn Pattern M24 Hellpistol. Each job specification in the Lunar Venatorii then also get assigned additional weapons and equipment based on their role in the regiment.