Darius & Family Timelines
It is worth noting that at the 9 years ago mark that the two being together was already "long ago" when the general regards Quill as the paramour to Darius. He also addresses her as the Mistress Varn, which suggests to me that she was an acknowledged lover to Lord Varn, whomever that may be. Decius is known to be her child, and likely it was assumed he was Varn's child. Many have concluded Quill was about to reveal the child to belong to Darius, which could very well make sense as we don't quite know what happened between the 19 yr ago and 9 yr ago mark.
It is not entirely clear how long ago Decius died, but it was after the last encounter Darius had with Quill 5 years ago. I don't recall if there was an age specified for the Noxus Draft, but it would have to be as low as 13 for Decius to be born shortly after that 19 year ago encounter and for the boy to have perished 5 years ago. It is quite possible, but that would highly suggest that her involvement with Varn would have happened within a year of that encounter, which would be a "long time ago" at the 9 yr mark.
Invetia is clearly the Daughter of the Varn household. It is unclear if she is Quill's daughter. Depending on how things unfolded, she could be the only child of Varn's first wife, whom may have died in childbirth or from some other random sickness. She could also have still been alive, but had fertility issues. I do think it reasonable to assume both Varn and this Wife have passed on at the point of the Rebellion, since Quill was in charge long enough to have her name written on a trade map.
My theory is that Invetia is the original daughter of the household and was born prior to Decius. Since it is clear the Varn household is from their home town, Quill was probably familiar with the Steward and courted him on the side. It is quite possible that Varn was well aware that Decius was not his child, but Patriarchy prefers sons and offered Quill the position of his Mistress in exchange for the boy. This effectively ended the relationship she had with Darius, which might have been fine with her. Hard to say. People do stranger things. I doubt this would sit well with Invetia, as she would learn the implications of these actions as she matured.
Now I am aware that Mistress could also be a Title, but this particular Mistress happened to run a whole city. I'm struggling to see how Quill would be handed control of a city even if she did earn war-hero status. This is why I feel a Lord Varn, whom was already established as the Steward of the city, is very convenient to assume exists.