What if there were two components to the Lance system? One where there are men in the population willing to join you, and the second was the means to equip them reflected by supply points. This way the lances would normally better reflect the peasants defending their town. You could expect to recruit a low level calvary or two, archers or some quilted armored spearmen. However, if you want them to level up and be geared more appropriately you have to take them to a place that has horses or armorers and get that gear and training for them. (a little like sword of Damocles)
These areas would generate supply points over time much like the lances that are bought with coin and take game time to implement. You might have the men and means to turn some veteran troops into advanced troops, but you will need to stand around for 2 days to do it. Some points could be available from looting as well, perhaps based on an enemy lords army size ( like renown rewards).
Essentially this would mean halting every troop tree at least once (maybe more) so that the men could come back and be refitted. Or maybe you could refit them from even the camp menu based on supply points, that would be a less of a pain. It could also give incentive to attack better equipped troops than you if you could loot them in some way.
This would be a devil, to have the NPC lords deal with this I fear.
Still, I feel that the lance system is easy and superior to Native in every way. If I were to change it, it would to be to make it harder in some way.