With this, Theron had successfully caught a corner of the deceased Patriarch's plan. In all likelihood, he had done this to confirm that Lyra was, indeed, the person he was after and could be used properly as a pawn.
But it also revealed something to Theron.
He was imagining a scene of a man, likely Lyra's father, who had quite the derivative habit of visiting brothels and philandering with women. And then he imagined a wife—maybe multiple wives, even—all of whom had a vested interest in making sure this powerful man they had latched onto didn't have more children to dilute their power further.
With that, Theron was fairly certain he had 90% of the truth.
However, there was definitely something deeper here.
If Lyra was just some child of a random prostitute, the Patriarch wouldn't be stupid enough to think she could be used as a pawn. Also, if Theron's calculations were correct, Lyra's talent was too high for her mother to be a nobody.