The Lannisters spare no expense when it comes to war.
Firstly, Lanniters are known for one thing, their deep pockets. Their riches allow them to pay only the best when it comes to arming and protecting their troops. On the other hand, halberds tend to be a relatively cheap weapon to produce, but those made for Lannister troops are still the highest quality, guaranteed to never break, even when under a charge from enemy cavalry. After all, these men are trained precisely to receive attacks, and they do it very well.