I really doubt that will be addressed even if we get a more direct confirmation of a Satoko/Lambda connection. In the main VN itself, all quotes that reference Lambda being behind Bern's tragedy work even more directly if they're actually about Satoko being behind Gou/Sotsu, rather than the original loops. Like how it was described as a "Contest of Endurance" and the same term was used in Gou to describe the upcoming Satoko vs Rika game; Bern saying that someone troublesome took a liking to Battler, and something similar happened to her when she was a human or the description about Bern being tortured by a witch in a labyrinth of despair. Everything there could apply to the original Higurashi in a way, but they fit Gou/Sotsu much more directly.
However, then we have Memoirs of Lambdadelta, originally published for an event in 2008 and then later republished in VN format as part of Umineko Tsubasa. This one is where it's outright said Lambda blessed a girl who wished to become god, with many quotes taken directly from Takano's speech about her certain will when she decides to study to take over her grandpa's research near the end of her backstory in Matsuri. And it's said that although the girl failed in the end her actions led to the birth of a new witch. This all seems like an obvious attempt to reference Higurashi within Umineko's context.
It could be a timeloop, which would preserve the meaning of the references (and R07 has referenced Tezuka's Phoenix as an example of the type of connections his series have, and Phoenix featured a similar recursive timeloop tying two of its stories together), but it also could just be something from an unrelated fragment, like when the adult looking Bernkastel at the end of Higurashi stops the death of Takano's parents. That obviously didn't change Rika's own world, it just created a separate one. Of course, this would weaken the obvious intended references.
I think the 2nd option isn't unlikely though. Gou/Sotsu themselves are shoving aside Higurashi's own Saikoroshi. It either didn't happen now, or happened but lost any meaning. In Saikoroshi, had Rika promised to leave her witch personality in the past, accept her next death, look at her current world as the one world, treating the other worlds she experienced as dreams, and speculated that her witch-self might still exist in a higher realm separate from her. This has been outright said to have been a Bernkastel origin story by R07 in interviews, and it was clearly the implication with Rika's random speculation about her other self still existing in a higher realm, but Gou/Sotsu are basically ignoring all that. Rika in Gou/Sotsu is driven by her experiences in previous worlds, never being able to leave the trauma from them behind, and clearly still had a witch personality within her (the red eyes scenes). So, if Saikoroshi is still meant to have happened, Rika didn't actually take any lesson from it and her speculation about her witch self was just meaningless speculation.
