The switching weapon rules don't even come into it.
For the most part yes, since we switch weapons only at the beginning of a round of combat. If a lance armed cavalry unit continually breaks or FBIGO's its opponent on the charge, it will never switch away from the lances, and can just keep using them.
But you aren't allowed to switch weapons in between rounds of combat, so there is a very unlikely edge case where not being able to switch weapons could come up.
So, if a cavalry unit wielding lances charged an enemy and they held, in the next player turn, since the cavalry unit did not charge, it must switch to hand weapons. Let's say in this turn somehow it did break the enemy unit (very unlikely to break them with hand weapons, if you didn't break them with lances) and the enemy fell back in good order, the knights pursued, and caught them. Normally they could use their lances, as it's a charge, but they have already switched to hand weapons and so cannot switch back. But if they still had their lances equipped they could use those.