Some Dot's proc thunderlords, like Darius's passive or a Teemo auto when he's level'd his E. Yet other dot's like gangplanks passive auto burn do not proc thunderlords. Also Brand passive doesn't proc it i'm pretty sure. Twitch's passive doesn't proc thunderlords but one quinn empowered auto does.
Point is, all of these are so inconsistent in my eyes, what're the differences?
The reason why some of the damage-over-time passives are not procing Thunderlord's Decree is that they are neither classified as an auto or a spell (effect). As the tooltip implies, you need either one of them or both applied for 3 times to trigger Thunderlord's Decree.
Darius' passive is neither. It's an on-action effect that is applied whenever Darius uses a basic attack or a spell.
Teemo's E is neither. It's an on-hit effect, not a spell effect. The very difference between Teemo's E and Ezreal's Q is that Teemo's E is an on-hit effect while Ezreal's Q is a spell that applies only on-hit effects and functions like auto attacks 90% of the time, except for structures, like all abilities that does not involve auto attacking and can apply on-hit effects.
Gangplank's passive functions exactly as Teemo's E, except it only works on his melee attacks periodically.
I haven't seen concrete evidence as to whether or not Brand's damage-over-time passive procs Thunderlord's Decree since it's a spell effect that functions like a spell. If it wasn't a spell effect, Deathfire Touch wouldn't apply to it at all since it only works on ability damage, which is almost the same as spell effects.
Twitch's passive is not a spell effect. It's an on-hit effect. This on-hit effect, again, should not be accounted an auto attack or a spell effect.
I know it's complex but I hope it will answer some of your enquiries. I also understand the interactions between the abilities and Thunderlord's Decree can be very inconsistent (Malzahar's E and Morgana's E for example. Morgana's E apply Thunderlord's Decree, but Malzahar's E doesn't unless when you couple that with Q), but I am guessing it's Riot's unintended oversight.
Malzahar's space aids doesn't proc it. But hitting someone with an E-Q combo does because it reapplies the space aids.
Teemos just started to too, it used to not.
