As written, the rules for mounted charges are beyond strange. I don’t know anyone who runs them as they’re written, and I don’t really think anyone should. However, given that they’re all we’ve got, they’re the only things we can analyze with respect to this question. How you choose to modify them to make them closer to most people’s conception of how they “should” work will necessarily also affect this question, and so anyone doing that would simply need to decide for themselves what they’d like the answer to this question to be.
Effectively, there are two different sets of rules that talk about mounted combat and charging. They seem like they were probably meant to align and work together, but they don’t.
If your mount charges, you also take the AC penalty associated with a charge. If you make an attack at the end of the charge, you receive the bonus gained from the charge.
(System Reference Document → Combat → Special Attacks → Mounted Combat → Combat While Mounted)
This rule says that your mount can charge, and if it does, you can attack at the end of it and get the bonus from the charge. It doesn’t say that you actually count as charging, yourself, it just says you get the bonus. Getting more attacks, as with pouncing charge, isn’t a “bonus,” per se, and certainly isn’t “the bonus” in context, which would be the +2 bonus to attack rolls you get from charging. Thus, under this rule, you would not get more attacks from pouncing charge. You would, however, get doubled damage from a lance—that says that your mount must be charging for you to get the bonus.
Enter the other rule, what maybe should have been the other half of one rule, but it isn’t:
Your mount acts on your initiative count as you direct it. You move at its speed, but the mount uses its action to move.
(System Reference Document → Combat → Special Attacks → Mounted Combat → Combat While Mounted)
So “the mount uses its action to move.” Which action? Unknown! Is that just always a move action, or is it using the same action you are? And if that “action to move” is a charge, is it charging? Does it get to attack at the end? Or just move like a charge, but without the attack on the end?
No one knows!
Regardless of what this means for what your mount is doing, this means you can charge while mounted. This is important, since the above rule (for when your mount charges and you’re just along for the ride) seems to prevent you from charging per se; you just get the bonus. This way, at least, you can charge, and so you can benefit from pouncing charge while mounted.
But whether your mount is charging or not at the same time is entirely unclear. But since it says “to move,” and not anything about any other action (like attacking), it seems to me that it’s not actually charging. But maybe charge-but-without-the-attack still counts as a “charging mount” for the purposes of doubling lance damage? We are deep into speculative territory here, because the rules are so vaguely written. In the absence of anything that says the mount is charging, or counts as charging, I think the “honest” conclusion is that it is not, RAW.
Effectively, RAW seems to be that there are two cases:
Your mount charges and carries you along with it, and you get “the bonus” from the charge but aren’t actually considered to be charging yourself. You can direct your mount to do that on your initiative count. Since you are on a charging mount, your lance damage is doubled; since you are not charging yourself, Spirited Charge doesn’t apply, and neither does pouncing charge or any other form of pounce.
Alternatively, you can charge yourself, directing your mount to move as necessary to trigger the charge. That means you’re charging and get all the benefits of doing so (Spirited Charge, pouncing charge, etc.), but your mount (probably?) is not charging, so it doesn’t benefit from charging and also doesn’t double your lance damage.
There’s more rules to pull in here, though, because Spirited Charge has something to add:
When mounted and using the charge action, you deal double damage with a melee weapon (or triple damage with a lance).
(System Reference Document → Feats → Spirited Charge)
First note that—unlike the doubled damage from a lance—this is triggered when you charge (while mounted), not when your mount charges. Second, note that it includes increased damage for using a lance—triggered by your charge and not your mount’s charge! This just screams “the author thought you charging while mounted and your mount charging were the same thing,” which would be sensible but isn’t what the rules seem to say. The tripled damage would match what we would expect if you combined the doubled damage from a lance charge with the doubled damage from Spirited Charge (under 3.5e’s rules for combining multipliers).
But instead, Spirited Charge seems to be producing a separate effect wherein lances do more damage on a mounted charge than other weapons. This is good, in the sense that it means you can actually benefit from, say, pouncing charge and a lance at the same time. It’s bad in that, one, the rules are clearly mistaken about how they work, and two, arguably, this separate effect could not stack with the doubling of lance damage when your mount charges, letting you get quadrupled damage instead of tripled. Assuming you and your mount can charge at the same time, which—RAW—you probably cannot.
This is all fairly well nonsense. The way everyone I ever interacted with on this subject has run things, is for both mount and rider to charge simultaneously, each using their own full-round action. That combines the lance doubling and Spirited Charge doubling for a tripling, as Spirited Charge’s parenthetical reminds us. The first quoted rule almost gets us to that, RAW—it might arguably seem to suggest that this is what they were going for, what they intended. But it doesn’t actually get us there, just saying we take “the penalty” and get “the bonus.” The second rules quote maybe could get us there, if “its action” is the charge action, but that seems like a huge stretch, RAW. But it seems very likely that you’re supposed to just be able to do both, or even that you must charge together in order to charge at all.
- Fun fact: centaurs should be an exception here! Both Races of Faerûn (3.0e) and Monster Manual (3.5e) say a centaur can use some things that require being mounted without actually being mounted. Unfortunately, Races of Faerûn includes Spirited Charged but not lances, while Monster Manual includes lances but not Spirited Charge. Since the Monster Manual version is a revision to the Races of Faerûn version (and it is, the update pamphlet says so and Monster Manual even changes a bunch of their other stats), you can’t—officially—combine them. So no matter which version you use, you still can’t combine doubled lance damage and the Spirited Charge feat.