Lets say I am playing veigar, the ultimate works as an execute. If my ultimate is the ability that triggers the thunderlord. What applies first?the ultimate damage or thunderlords? If thunderlords applies first, then I get more damage on my ultimate. I want to know if it makes any difference in calculations.
Thunderlord's Decree works based on taking damage from abilities and auto attacks. If no damage is taken, no stacks of Thunderlord's is applied. The only exception to this rule is for damage over time abilities, such as Twitch/Cassiopeia/Teemo/Singed poison, Fiddlestick's W (drain), or Swain's E (torment).
This means ability/auto attack damage must happen before the full proc occurs. So when playing Veigar, when using his ult, Thunderlords happens after the ult hits and thus does not increase the raw ult damage.
From the wiki:
Hitting an enemy champion with an ability (ability damage) or basic attack (on-hit) marks them with Thunderlord's Decree for 3 seconds.
That means that Thunderlords' damage will be applied as soon as the third mark is applied.
Since the mark is applied after ability damage or on-hit damage, then in your scenario, Veigar's ultimate will be the third mark and Thunderlords will damage after the ultimate damage.