I don't understand why anyone would want to use Lilims as subs... even if you consider on-element bonus, it's like 1650 atk vs. 2000+ atk for good off-element Eidolons. In other words, the stats are pitiful. The on-use is... okay-ish, but on a long cooldown and nothing special.
Mind you, the most Elemental attack you can gain is 45% elemental advantage + 90% Eidolons (excluding P2W) + 30% Relic. This means 165%. That's more than what you have for Assault, so Atk Up buffs become stronger than Elem Up buffs. If we take elemental advantage and Relic weapons out, then yes, Elem Up buffs are quite strong since 90% Elemental attack will be far less than your Assault.
Anyway, what makes Kaisers special is:
1. Only 8 turn CD, so ready quite fast for an Eidolon
2. Gives you a hefty amount of damage cut against the opposing element (not sure what the value is here, 30% at LMB?)
3. Gives you a hefty amount of Elem+ (30% at 0-stars, 40% at 1-star)
4. the stats are alright at 0-star (around 1600 before same-element bonus) and already around a whopping 2000 at 1-star.
Meanwhile, compare to Lilim and it's like... bad stats at LMB (0-star Kaiser is all that most people will have and is around the same, though!) and only 10% Elem+ with a long cooldown. You're just better off with something else, like Tiamat/Ygg/Sphinx/Mii.
tl;dr; Assuming that you ever use Eidolon active abilities, Kaisers are good enough to make it to your team at 0-star (same element), but get REALLY good at 1-star (same element). Meanwhile, Lilims are trash. Something you might use as a new player, but nothing else.They don't. I haven't tested, but I'd be shocked if they did. They're both elem up+ Eidolon frame.