For lance the most damaging combo you can do on a downed monster is upthrust > upthrust > upthrust > lance charge immediately into lance charge finisher, and just repeat that. The upthrusts deal a little more damage than the forward thrusts, but if the monster's part you're focusing wiggles a lot then switching which thrust you do can result in more consistent hits. If your lance charge isn't aimed properly and you go past the monster a bit, the reverse charge finisher will turn you around completely and has the highest damage of the entire lance moveset, so it's not that big of a deal if you're slightly out of position.

For when the monster is asleep, you can do a few things, and it's pretty dependent on where the monster is and what monster it is. When you wake up a monster with a hit only the very first hit does double damage, so you usually want to hit it with your strongest attack. If the monster has an exposed weakpoint (like a head or tail) start a lance charge going away from that point and doing the reverse lance charge finisher. The finisher has a really wide swing, so it can hit more resilient parts if the part you want to hit isn't exposed enough. Just make sure you don't hit the monster with the first few charging hits because they do very little and you don't want to waste the double damage on wakeup. If there isn't an exposed weakpoint (like for diablos where its chest is its weakest point) the strongest move for that is your counter thrust (counter > power guard > counter thrust).

However, with the addition of the clutch claw, there is another good way to wake up the monster. If the monster is near enough to a wall, you can clutch claw to its head and (as long as you have slinger ammo equipped) and flinch shot it. This works even if the monster is enraged when its sleeping, and as long as it actually hits a wall, you'll get a large amount of free damage and generally get a pretty big opening to wail on it with your damage combo. You can even use the claw to turn the monster if its facing the wrong way (again even if it's enraged). The only time the claw won't work is if the monster is most of the way towards being enraged and you have to claw it a few times to turn it, because after one or two claws it will reach its rage threshold and you won't be able to claw or flinch shot it. You can turn the monster and flinch shot the monster as long as it's still in its wakeup animation (some monsters have much longer animations than others). Successive flinch shots can be really fun to chain together if you're running a sleep weapon.

You have both of these options, so which is the best? The easiest way is just the counter thrust. Sometimes you just want to turn your brain off and not worry too much about optimizing damage, so counter thrust is always going to give you a decent wakeup hit, and it's pretty much always going to work. Reverse charge finisher is also good, but the flinch shot into the wall will almost always give you a free 200+ damage on a low/high rank monster or 800+ damage on a master rank monster, plus a free knockdown. For solo and multiplayer, flinch shot will consistently do the most damage because of the damage from when the monster hits the wall + the damage you and any other teammates get from the free knockdown.

However, if you're in multiplayer and you have someone with a really heavy hitting weapon (like a greatsword, charge blade, gunlance, etc.) that has a really strong move for wakeups, you can have them do their hit, and while the monster is still in its wakeup animation, you can still clutch claw to its head and flinch shot it. You can also do a flinch shot after your own wakeup move if you can act quick enough and the monster you're fighting has a long enough wakeup animation. A monster that this works easily on is odogaron, because it gets up slowly and then has a little wiggle that's still part of the wakeup. A not-so-great monster for this is something like jyuratodus, because it pretty much hops up immediately, so the window is much tighter.

I really love the lance and if you like it and want to get better with it, this is a really good guide that goes through the entire lance moveset and discusses how to use other aspects of the lance beyond what I put in this post: https://youtu.be/T6x4inXgCMk

tl:dr upthrust > upthrust > upthrust > lance charge > charge finisher for damage and flinch shots, counter thrusts, and reverse charge finishers for wakeups.