I have thought out a late tier 2 upgrade for overlord. One of the overlord's upgrade from zerg lair is called Ventral Sacs. In SC1, this upgrade gave ability of transporting units to overlords. In SC2, in addition to ability to transport units, this gives the overlord to produce terrazine gas that will make the hp regeneration of zerg ground units around the overlord faster(As in really fast, 1+/15seconds!). Like those auras in WC3. P.S. I just realized this means that overlords fart to heal their comrades. (Aw F%*k! Overlord Fart!)
....Why would Terrazine heal them? It's like....Napalm. Anyhoo, we've got an aura thread. Talk about it in there.
No healing please. Zerg healing was never meant to give them the upper hand during battle. Healing was only there to emphasize their organic matter and to recover from attacks and thus compensate for them being weak in general.