There is absolutely no consistency in what counts as a stack. Lux, Bard, and Lulu AA's with Passive: 2 stacks. Teemo AA with E: 1 stack. Morgana W: 1 stack per half second. Malzahar E and Ult: 1 stack. Teemo Mushroom: 1 stack (after some sort of delay). Malzahar's Voidlings: 0 stacks.
So there's just seemingly arbitrary things that count as stacks while others simply don't.
In my opinion, Riot should remove Thunderlords Decree mastery and replace it with a new mastery. One that has a clear "I should only be picked by X" identity and which is easier to balance. The current T/L state is a nightmare. Most mages pick it. Supports pick it. Top Laners with damage-focus pick it. Junglers pick it. Hell, even most ADCs pick it.
WTF!?!
Auto attacks and spell damage (in most cases, there are some exceptions) can tick Thunderlord's.
In the case of Lux, Bard, and others with similar passives, their auto attacks also apply spell damage through their passives which ticks Thunderlord's. Teemo's poison doesn't apply spell effects (it hasn't for a long time), which disqualifies it from ticking Thunderlord's. Lulu actually works the same as Teemo, her passive doesn't apply spell effects either.
AOEs like Morgana W and MF's E apply multiply ticks because they (and other similar effects) apply multiple instances of spell damage. Regular debuff DoTs like Malz E or Teemo shrooms only apply one tick because it's one continuous spell damage.
So yeah, Thunderlord's certainly seems weird but I hope this clears somethings up.
From what I've found out, Dot effects can't proc Thunderlord's.
Don't forget Miss Fortune's E as well. Seemingly able to get Thunderlord's with that skill rather easily.
i was really confused last game cuz i was playing 
with thunderlords and i distinctly remember getting #rekt by DoT's stacking thunderlords on me and chunking me before, yet my bleed didn't apply thunderlords at all and it seemed like my W only applied it once (even without DoTs applying it i would think abilities that hit twice should)
they should probably make it consistent.
Wait, Lulu AAs only apply one stack; Pix doesn't apply spell effects or on hit effects. Thunderlord applies from on hit effects and ability damage. The only limitation would seem to be targeted DoT effects, because there's no counterplay besides not getting in range to get hit.
I agree it's a bit confusing what does and does not apply stacks though; it does, however, mean that certain champions benefit more from the mastery than others, which is kind of the goal of the new mastery system. The problem, as you said, is still with the readability of some of these things. I think it's limited in some cases and allowed in other cases since it's a little more difficult to proc in certain circumstances, like if Pix applied stacks with every instance of damage, it would be ridiculous since you'd get it with a single auto attack. On the other hand, Lux needs to land an ability to get her passive, which at least costs her more than a single auto attack (and it means she needs to get a little closer to the enemy, where she's typically one of the longer range mages). Similarly, Bard's meeps have a cooldown, so it's not every singe auto attack like it would be with Lulu.
The worst thing about Thunderlord's that a single ability (MF's make it rain for example) can proc it.
The problem is that there aren't any masteries that can compete with TLD.
Deathfire is a niche that works great on a select few DoT champions and awful on anyone else. Fervor takes too long to stack up Warlord's was nerfed.
What else is there to take? Even supports can take Thunderlord's because it scales mostly with levels and not AP, while Windspeaker's increases Shields/Heals, and thus is indirectly dependent on AP, which a low-budget role can't build effectively. The damage given by Thunderlord's simply outclasses the utility of other Keystones.
For a moment I thought you were gong to say: "Everyone is using it"
But this is also irritating.
Well Teemo doesn't get DFT from his E either. Disappoint.
It's simple really. Just ask "is it a debuff?".
Malzahar's E is a debuff applied once that lasts 4 seconds that deals DoT, and as such applies only one Thunderlord's proc.
Morgana's W is a damage field that procs every second, every time applying a proc.
If the debuff is associated with another source of damage it will not proc. Lux's illumination does not proc if damage isn't dealt, and teemo's E is a debuff applied by his autos, and as such it never procs at all
Ryze e procs it immediately if there are minions around.
Ziggs passive one stack, Quinn passive 1 stack but was 2 previously, not sure when changed. I think fiora passive still 2 stacks but not sure.
It doesn't take a rocket scientist to understand how Thunderlords works...
Every AA counts for a stack, Every spell counts for a stack depending on how many parts there are. For example
Akali Q + Auto is 3 stacks because the initial mark applies a stack, then when you detonate it the AA AND Detonation count each as a stack.
Katarina, very similar to how Akali works. Q a target then explode it with W cause the initial mark counts as a stack, then the detonation and Sinister steel both respectively count as a stack each.
Lux E + AA or any target with her passive on it will count as 3 because it's like a mark. Q, + Passive + AA. Since passive is an ability it applies a stack
I find it pretty consistent.
Every time something is activated, it adds one stack.
Lux's spell (any) adds one stack Lux AA adds one stack Lux passive adds another stack when explodes. Hence, one spell + 1 AA procs thunder.
Teemo E isn't a spell but AA enhancement, hence only 1 stack.
Fizz's W on the other hand, is AA + one activation, hence his AA adds 2 stack.
Malz E adds 1 stack, because it explodes only once. Malz W adds one stack everytime it ticks, because it ticks multiple times.
Thunderlords decree should just work like ludiens ekko
Dealing damage casting abilities and moving increase your stacks by 3/6/9/12 (increasing at lvl 6/11/16) (auto attacks grant half stacks) Stacks to 100 and on 100 stacks your next ABILITY used procs thunderlords decree dealing 10 +1.0 bonus ad and .65 AP to the closes 4 targets of your primary target (does not increase damage to primary target)
This effect will prioritize champions over minions however it deals 200% damage to minions
This gives an AoE option that is good for wave clear and team fight aoe favoring champions, and it is more focused on casters because it is a spell cast to trigger it and AAs grant half stacks (due to AS late game on ADC would make it broken for them otherwise)
