If the Lannisters are known for one thing, it’s their deep pockets. Their wealth lets them afford only the best when it comes to arming and armoring up their troops. Halberds tend to be a relatively cheap weapon to produce, but those made for Lannister troops are still of the highest quality, almost guaranteed to never break, even when receiving a Charge from enemy cavalry. And receiving a Charge is just what these men are trained to do, and they do it well.
On the battlefield the Lannister Halberdiers are a force to be feared. With a move of 5, armour of 4+ and a morale of 6+ they can be positioned in such a way that the enemy has no choice but to charge them and this is exactly what you want. The Halberdiers are built to take a charge. With 7/7/4 attacks and the special rule set for charge, the Halberdiers get to strike the enemy before they can take any casualties themselves. They also have the sundering rule dropping the enemy armour by 1.
The Assault veteran is a great attachment for the Halberdiers causing the enemy to take morale tests at -1 and also causing a wound on the enemy if they fail a morale test.