The Kraken would like a word with you
The Kraken has a fling action that reads:
Fling. One Large or smaller object held or creature grappled
by the kraken is thrown up to 60 feet in a random direction
and knocked prone. If a thrown target strikes a solid surface,
the target takes 3 (1d6) bludgeoning damage for every 10 feet
it was thrown.
In its case, the throwing is not straight down, but that is not the point. The point is that the kraken has a special action for it. Other creatures do not have a throw ability that allows them to throw down a grappled creature in a defined way, so this is for the DM to adjudicate.
The rest of this answer tries to explore what useful adjudication can look like within the rules, to help make a call with that, but it only provides suggestions.
Can you lift them up? Lifting something is covered under Lifting and Carrying (PHB 176):
Push, Drag, or Lift. You can push, drag, or lift a weight in pounds up to twice your carrying capacity (or 30 times your Strength score).
This rule contradicts the grapple rules, as the grapple rules only care for size, not for weight. (As Jeremy Crawford also points out, although of course in no official capacity) Maybe the grapple rule assumes that the grappled creature stumbles along, even if it is too heavy for you to lift up. Grappling allows you to drag and carry, not to lift or push, but carrying implies you can lift whatever you carry.
The DM needs to resolve how to handle that contradiction. If the DM concludes lifting can be treated like dragging, you can lift a grappled creature and it has no say in the matter, just as if you would drag it. If the DM concludes that the lifting rules apply, you can only lift them up if you can handle the weight.
The grappling rules say about the target in grappled condition:
The condition specifies the things that end it, and you can release the target whenever you like (no action required).
So, once lifted up, you can just let them go.
However, releasing the target that you lift up may not mean it would free fall -- the most natural way to lift someone up is straight overhead, so they would just fall on you, and from less than 10 feet unless you have really long arms. So you need to actively throw them down. The default action for that is a shove attack:
Using the Attack action, you can make a special melee
attack to shove a creature, either to knock it prone or
push it away from you. (...) The target of your shove must be no more than one size larger than you, and it must be within your reach.
You make a Strength (Athletics) check contested by the target’s Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the ability to use). If you win the contest, you either knock the target prone or push it 5 feet away from you.
The only difference is that you now knock them prone from a height, so they will take fall damage too, 1d6 per 10 feet fallen as per the falling rules (p. 183 PHB).
I think from a balance perspective, a ruling that allows you to just lift them up and drop them for free when grappled would not be broken: for comparison, you can grapple a creature when you have a flying speed, assuming it is light enough if you care about weight, fly up with them and drop them from there, potentially dealing a lot more damage.
Also a huge giant who might be able to drop you prone from a height of over 30 feet for 11 (3d6) damage would use their Action to grapple for that, when they just as well could hit you with their greatsword multiattack for two times 30 (6d6+9) damage. That seems like a reasonable trade-off.
