I did many test runs (hey its free so why not) and only included the prime examples in the videos, but the tests are consistent with what you see in the video.
1. Switch to skills that apply CC, we typically take Dash and ShadowStep with the faster cooldowns so we can run content faster, but for lilith you want the CC enhancements, they make a difference.
2. Use different tempering on each item (It's alot to ask, I know, given how hard to roll gear is but it just works).
3. Do not attack Lilith after you brought her HP to 0 in stagger phase, otherwise she will cast her abilities even after you "killed" her.
4. For high Pit pushing, this tactic is not a big deal, you can't stagger bosses many times anyway and regular mobs get CCed easily, so prefer to take Dash with cooldown.
PS: I did this only because I swapped gear and got upgrades with duplicate tempers and noticed I wasn't staggering lilith anymore, so that prompted the whole test :)
#Chapters
00:00 Test 1
00:18 Test 2
00:44 Test 3