Vrill II ( Brainiac his father is Vrill also) is only a 10th level Genius. Lyrl is a 12 but he lacks the maturity of the others as well. Brainiacs best mental feats are well below the best of B5 who lets face it while an equal level intellect has another 1000 years of technological development to draw upon in his work. expounding on this much greater level of development with the same level of smarts has to ( and does) translate into greater feats.
hardly. getting completely and utterly defeated by the trickery of a lower level intellect ? his son) despite having all the cards at your disposal ( he had complete access to the coluan data core, so essentially ever mind on the planet including Vrill II) is hardly a great showing. Kot when you compare it to conquering War world, defeating Galactic empires, and the like of story lines like Panic in the Sky where Brainiac single handedly took on many of earth heroes including Supe's Maxima and 4 or 5 GLs (IIRC anyway)
fist it was far from a team up. Lyrl was tryin to take over Colu exactly the same way Brainiac was also. it was actually a three way battle where Vrill II joined Lyrl's attack ( knowing it woulf fail). Brainiac actually defeated them both as Vril knew he would. having then captured his son Brainiac discovered a secured part of his mind that he could not access. he probed deeper and deeper until he broke through and fell right into Vril's trap. Vril had placed all his pent emotions of rage, disgust, hatred, sadness etc within the secured part of his mind. once Brainiac broke through he was overcome with a flood of powerful emotions he could not deal with. Vril pretty much beat him alone when he held all the cards. Lyrl was useless.
Brainiac has conquered an empire or two one at a time, but IIRC Kang has conquered multiple empires at on e in multiple time lines. hidden himself from abstracts and more. Now B5 has feats like that against Time Trapper etc but I would say he has to fight for a win here. Possible but not easily and no guarrantee of a majority.