There is no maximum. You can always engineer the situation to require additional dice.
For instance, a hunter ranger can use Volley or Whirlwind Attack to attack “any number of creatures within [10 or 5, respectively] feet.” The spell prismatic spray says “For each target, roll a d8.” There are, no doubt, more options that have your roll a dice for every creature in an area, these were just two options off the top of my head. And there is no limit on the number of creatures who can fit in a space if they all get along. So no matter how many dice you have, you can find yourself needing even more dice because there are still more creatures to attack. A reasonable DM will apply a limit on creatures squeezing into a space, but that’s their ruling, not part of the rules, and so that number is going to be different for every DM (and likely vary with any given situation).
Since Volley and Whirlwind Attack have you making attack rolls, that involves a d20 for the attack, and then can involve any size dice in the damage roll. (None of the simple and martial weapons in the Player’s Handbook deal 1d2 or 1d3 damage, but that’s easily handled by also using magic to turn into an animal that uses those dice for damage.) Prismatic spray, of course, uses d8s. So you potentially need infinite dice of every size in order to successfully complete these actions. No weapon uses percentile dice (d100), but since percentile dice are rolled by rolling two d10s, that doesn’t change the answer as we already need infinite d10s for a Whirlwind Attack with a halberd or pike (or a Volley with a heavy crossbow if you have Crossbow Expert).
Also, neither delayed blast fireball nor meteor swarm requires 144d6 dice. If you’re talking about something like, having nine 9th-level delayed blast fireballs going off in the same turn that you cast meteor swarm, then at that point you’re combining multiple actions and effects and there really is no limit. Also, that adds up to 225d6 so I’m not sure what you’re talking about (limiting yourself to the spell slots that someone could actually have, and using two 7ths, an 8th, and a 9th for this, results in a maximum of 104d6).