I am honestly a bit... confused how the Dox bloodline in conjunction with the Brainiac title works on Colu because there are two contradictions that seem to cancel each other out. Also I have suspicions that have little evidence but I ramble about anyway.
What the comics are consistent on is that there is a very clear line of succession with the Brainiac Title; it goes simply 1, 2, 3, 4, and 5 all under the surname of Dox and it is passed from generation to generation. Keep in mind, I am referring to the PZH reboot here.
Legion of Super-Heroes (1989) #119
Mon-El: You should have seen his great-grandfather!
Gear: He's still alive?
Mon-El: I doubt it... But we haven't seen him in a thousand years.
This scan is a little blurry but in this issue they talk about Querl (Brainiac 5) and his ancestor (Brainiac 2) as being his direct great-grandfather. This suggest that between Querl and Vril there really was only 2 others and no more.
We already know that Vril Dox II had his son Lyrl who took up the name Brainiac 3 on his own accord and with this clear line it makes sense that at some point he had Querl's mother Brainiac 4.
Because Coluans live for centuries it is not impossible that Lyrl had his daughter late or that Coluans simply created her from his own genetic material, there is no limit as to how she was born. Also ngl it is absolutely within the realm of possibilities that Brainiac 4 could have just been created to serve a roll and Lyrl didn't intentionally have any children.
That is all speculation however and shouldn't be considered as any sort of canon.
Where things about this clear line get weird though is earlier in the series when Querl talks about his family history with Colu.
Legion of Super-Heroes (1989) #77
Querl: Many years passed before the bloodline resettled on the home-world -- and toiled for the planetary interest. Secretly loathed by the jealous normals we served... ... We were nevertheless treated as royalty, or state property... until the Brainiac 4 scandal and the governments subsequent destruction of all related records.
With how Querl talks about the series of events he seems to be either implying that after Lyrl there were more generations until eventually one decided to come back to Colu where then they were subjected to varying degrees of treatment.
The theory that Brainiac 4 was created by Colu instead of actively pursued by Lyrl sort of holds when you find out that after she abandoned Querl at birth the government just purged her records entirely - perhaps out of shame or just to cover up that they might have made some sort of error in her creation (it was Vril's fault actually but no one knows that yet).
But ignoring that the above seems to imply that after Lyrl, there may have been more generations and which case if there were... why were there only a couple more Brainiacs?
The other interpretation is that Lyrl himself came back to Colu eventually and because Coluans live for centuries this is not impossible. Querl could have been referring to that Lyrl was treated as royalty while his mother and himself were treated as property (because maybe Brainiac 4 was no intentionally born).
Honestly because Coluans can live for centuries I feel like it is absolutely possible that the line really did only have 5 generations.
The harder sell to this is begging the question WHY Lyrl would ever go back to Colu due to events in R.E.B.E.L.S. (2009) solidifying that he'd probably rather eat light bulbs every day than go back - but that Lyrl was only a teenager and a lot can change in centuries.
The other option is Vril Dox II had more children himself and the line just picked up, perhaps ignoring that Lyrl called himself Brainiac 3, and Lyrl is not even counted as an official Brainiac but again that is entirely unsupportive speculations.
