I mean, there's a certain level of balancing needed to at least be attempted when running a quest. While it is technically possible for Nakai or Oxyotl to just sort of...show up whenever they want, it'd sort of be a bit crazy if they DID do that just whenever. I already have gotten guff that I'd like to not have to deal with again, just having Deus Ex Lizard pop up whenever Chaos is doing something would undoubtedly lead to just...me ending up having to read stuff that would be frustrating and/or hurtful or something.
You also have 'The Great Plan of The Old Ones' to hide behind, as in the lore the lizardmen have messed up before, as well as had debates on what exactly they should do now that the Old Ones are gone. The lizardmen aren't likely to just pop in one day out of complete nowhere, without some form of "The Plan Said" related to their actions. Though the lizardmen do have members that do their own thing that is not included in The Plan, such as raising a mountain range to block out druchii. But those are exceptions, are really radical slann, or have a immediate purpose.
Lizardmen mostly keep to themselves in the Southlands, and Lustria. Lord Hua-Hua did win that 500 year old debate about what the lizardmen should do about the younger races. Isolation and retaliation upon attack, or theft, as a societal policy seems like what won, with the main exceptions being anything the Great Plan says needs them outside of their temple-cities.
A Beast-tide of beastmen like what Malagor is doing is not likely to attract the Lizardmen. Before the Empire was a thing, beastmen were a problem and it didn't attract the lizardmen then. Much like how the massive Quiet Whaaagh, hasn't had the hint of lizardmen assassin attempts (With the skinks of the Southlands being so relatively close, the fact they didn't try, says something). The Lizardmen aren't really a active faction trying to plug in the potential Doomsday scenarios, so much as they let the crisis get extremely bad before they take action, the whole world must be about to face a crisis, not merely your continent, before trying solutions.
The Lizardmen were unaware of the goings on at Albion, I think you said in your explanation on the oghams and the Albion ritual to support the Vortex. But I do recall how you said that the Albish doing the assist was not part of the Old Ones Plan, thus the Lizardmen would not know or have anything related to Albion going on at all in the Great Plan. Hmm, though the fall of the portal gates wasn't part of the plan either.
Edit: There's also the False Moon War in I think 2418 IC where the Slann Mage Priest Tecciztec enacts a ritual aimed at pushing Morssileb out of orbit, it's kind of successful (shakes chunks of the moon off, that land onto Mallus), and only fails due to insufficient power. Though the lizardmen had been fighting against the moon off and on for millennia.