If a horseman's lance was stuck, broken, or simply dropped in the sheer shock of an engagement, then they would pull out another weapon to defend themselves and keep fighting. Sometimes a spear was lost because the horseman threw it into an infantry formation in an attempt to break up the line. If the cavalrymen were able to pull out and get back to their own lines, then they might be able to grab a spare lance from an attendant. But most horsemen would generally carry other weapons with them besides a lance, most likely one-handed weapons like a sword, axe, mace, or hammer/pick. These would also be useful in the event that a cavalryman was dismounted (either by choice or because his horse was killed under him) and had to fight on foot.

Breaking or losing a lance during the charge was generally the norm. At the end of the 16th century an argument often made in favor of pistol cavalry was that a lance could only be used once while a rider with two pistols could fire twice and then reload later. Especially as they grew longer and heavier a lance generally wasn't very useful in a melee once the charge lost momentum anyways.

There were exceptions though. During his conquests against the Aztecs Cortes was described as having to give his cavalry specific instructions to keep a firm hold on their lances and to be very careful that they didn't get stuck or grabbed by the enemy, because Cortes had only a small number of horsemen and not that many spare lances.