That may be the case, but for some of us it's hard to just snap a finger and pretend the original timeline dosen't exist just cuz Cox says to. Especially when they have recurring characters...it's difficult not to make connections somehow.
That's what fanfictions are for. Hell, look at the timeline now, with IGA and all the other games. People choose and pick what they want in the series, making their up their own timelines to reflect what their ideal vision of Castlevania. You have people trying to fit in CotM, Legends, CV64 and LoD(even the Resurrection, which wasn't even released) into IGA's canon. Surely working LoS into it, as well, can't be much harder than THAT. Just write it as fanfiction! It's a no-brainer, really/
Just say, like, the Cornell in LoS is the great ancestor of Cornell in the LoD(which he was named after). Carmilla's age, like Dracula in the CV series, can be open to speculation. I mean, in CV series, Dracula was DIFFERENT than his real-life counterpart. He was OLDER, and by the time(in our world) where Dracula was ruler of Romania, he was an old vampire lord(in CV's world). Same for Carmilla, who, I don't recall ever having a specific age tacked on to her character in this series. It could be possible that she IS older than Dracula. I mean, in IGA's timeline, Dracula was never the first vampire. Walter was older than him. Also, regarding Laura, in the novel of "Carmilla", she was a teenage girl living in the 1800s, but in RoB, she was a woman living in the late 1700s. CV's depiction of her is not unlike that of Dracula, so Laura in CV isn't bound to the novel's specifics. In CV, like Carmilla, her age isn't given, and she could very well be some girl Carmilla abducted in the early 11th century, is turned by Carmilla and acts as her vampire slave/daughter. An interesting thing regarding Carmilla in LoS is that her face has a similar look to the model we seen in DXC.