Theory About Lila
Based on the first screenshot, we see a figure, similar Lila's ancestors when undergoing 'The Agony", standing with Lila in the secret room. This could be how Dorotea gets control of Lila. We still don't know exactly what Lila is honestly.
In the second screenshot we see Tula off world. Being that she was put in charge of the school until Valya returns, there has to be a serious reason for that.
In the third and fourth clips we see Tula talking to Jen about a "time of crisis" (you can read her lips) and we see Jen visiting Lila who looks locked in a room.
In the fifth clip We see Lila leading Avila and other sisters through what looks like the corridor to the secret A.I room.
In the sixth clip we see the sisters and acolytes seemingly watching someone leave and Emeline, who seems to be picking up Dorotea's old teachings, is at the forefront.
TDLR; I think Dorotea gains control of Lila and forces Tula to leave the school with any sisters loyal to Valya. I think Tula may get a copy of complete breeding index before she's "exiled". I think because Jenis headstrong and seems to be an independent thinker, Tula trusts her to not fall into Dorotea's cult and Jen helps the Harkonnen sisters from inside the school.
Valya gets her wish and reunites with Tula as they're forced to fight a battle on two fronts.