Do you think that Beta was extremely lucky when Ainz shouted "you fool" and "disappointed" at her? Because if there had been other Guardian(s) beside Mare at the scene, especially Albedo, she would have been killed right at the scene even if Ainz had pardoned her.
If we are speaking about the side story, let me correct you first in saying that the NPCs present were Aura, Narberal and Sixth.
Similar situations have been presented to us prior to this point in the light novels. (Examples being both the situation regarding Cocytus’s defeat at the battle of the Lizardmen and Sebas’s ‘trial’ to prove his loyalty. The prior being more of an example for the question at hand.)
We’ve already seen how Albedo reacts when it comes to addressing perceived failures in the chain of Nazarick’s command. She treats Ainz displaying even the slightest hint of disappointments as a direct slight against him, and as such she reacts as you’ve mentioned: Bloodlust. Yet, something as simple as Ainz talking her down, correcting her, or presenting word of mercy towards the NPC at fault have been shown to dissuade or even dissipate any sense of malice towards the offending party in Albedo’s eyes. When it comes to Albedo, Ainz’s word is absolute, thus his mercy is as well.
If she hadn’t been in 'time out’, things would probably mirror the interaction between Ainz and Albedo during Cocytus’s reprimand. Ending with Albedo thinking highly of Ainz for his mercy over such 'flaws’ Lupusregina Beta displayed, and/or rationalizing it so that is somehow falls under Ainz’s plans. Cue the 'Sasuga Ainz-sama!’.
The only thing Beta was lucky for was she didn’t have the extra stress of dealing with Albedo’s dagger eyes.