Broken Lance can be repaired to its original weapon at the blacksmith. Check the original weapon for the repair cost.

All Lances become a Broken Lance once you run out of uses. You should try to repair or forge your Broken Lances, but there is utility with Broken weapons. Because of their low Mt and Hit, they are exceptionally good at farming Lance ranks and Class Mastery (though unequipping is better for just class mastery) in Auxiliary battles, as your units will barely deal any damage to enemy units.