Let's do some simple math.
Anivia has about average attack speed at level one, but abysmally low attack speed at level 18, and is at best below average for attack damage at all levels. Because she has below average stats for auto-attack focused builds, and none of her abilities scale off of anything but ability power, a good damage build on Anivia only includes AP, not AD (with the rare exception of a Hextech Gunblade, but that's an insanely situational build, and you don't build it for the attack damage).
A typical build on Anivia results in her ult doing about 170 damage per second (80 base plus about 90 bonus (from 12.5% of 720, which is about typical end-game AP for her)).
At level 18, her AD is 106 and her attack speed is roughly 0.8, which means she can make a total of 5 attacks every six seconds, and on average deals 88 damage per second with auto attacks every second if she's continuously attacking, meaning that a standard build will result in her AA's doing about 51% of the damage her ult does in the same time against a single target.
Warlord's Bloodlust caps out at 15% life steal at 80% missing HP. 15% of 88 is 13.2, so if you're at 20% or lower HP remaining, you'll heal 13.2 HP with an auto attack and Warlord's, but only if it's against a champion! If it's against a minion, then you only heal for 1/4 of that, or 3.3 HP, which actually is lower than your health regen at level 18 with a normal Anivia build. If it's against a structure or monster (non-minion non-champion), you heal nothing (lifesteal and spellvamp don't work on damage to structures, and Warlord's doesn't work against monsters). Once you take the averages (because no sane person is going to run around with only 20% HP all the time), you only get 7% lifesteal out of Warlords, which halves all the healing above, and thus means it has nearly no effect for Anivia.
Now, by comparison, if you instead get Thunderlords, a typical build will give you (at level 18) an extra 250 damage every 15 seconds, or Deathfire Touch will get you an extra 95 DPS on your ult, both of which will kill the enemy faster, and by extension, reduce the amount of damage you take (the faster you kill a target, the less damage they can deal) and therefore reduces the need for you to heal proportionately.
all warlords.
Warlords is the thing man.
