A lot of them might be lateral thinking puzzles - but some are just... Entirely unclear. (The worst of them sure looks empty, which is Suspicious.)

Maybe the library has Clues? Or they could go back to that one with the rosebush and try poking it more. The flower was nice.

'Nice flower' is as good a reason to start there as anything. 

Nice!

As they're navigating through the facility in that direction, Babs abruptly stops the group and pulls her rapier.

Out of the gloom of the entrance tunnel, two figures approach. One tall and hulking, the other slim and indistinct.

They resolve into Dulcinea Septimus, wrapped in a shawl, and her cavalier Protesilaus. "Ohhh!" the Duchess flutters. "Is that you, Third? My goodness, you gave us a shock. It is rather dark down here, isn't it?" She gives a giggle that ends in a wet cough.

...You'd think a dying invalid would make more noise as she moves. (Leia tenses a little when Dulcinea and Protesilaus appear, but doesn't let herself flinch.)

She makes herself smile, slipping under that regal mask. "It's a marvel there's any lights at all."

"I knooooow!" Dulcie trills. "You don't think that's one of the secrets of lyctorhood, do you? Seeing in the dark?"

"Navigating in adverse circumstances, perhaps."

"What a clever turn of phrase," she smiles.

"Speaking of adverse circumstances, have you done very many of these labs, yet?"

She pauses to think about how much to reveal. "We were investigating a few just now."

"Have you been by Lab Eight yet? I think I know how to solve it, but I'll need some help."

"We've looked at it," she acknowledges. "We were thinking of doing a few others first." Still, if she's offering... "If you know the trick to it, though - " She glances at her sister and cavalier. "We don't mind looking at it with you."

"Oh, wonderful!" She smiles twinklingly. "I was so hoping you'd agree. Let's go!" And she and her cav will set off towards the lab.

They'll follow! (She'd thought the Duchess was supposed to be sicker than this - perhaps the First House is good for health, somehow, or perhaps their intelligence was wrong.)

Septimus volunteers no answers on her own.

Laboratory Eight is labeled DIVERSION - PROCEDURAL CHAMBER. Below the tag, another person has painted, in smaller letters and fancier script, AVULSION!. Inside, the room slopes downward to a thick metal grate. The Seventh hobbles over to the wall and flips a switch that causes the obstacle to rise grindingly up into the ceiling. Beyond the grate is another corridor, looking to be at least a hundred meters long and seemingly empty except for a plinth with a small box at the far end. Where the grate was resting on the floor is painted a thick strip in bold black and caution yellow.

She brought a pole specifically for poking things with - she extends it past the yellow and black line, intending to prod the ground in case there's anything activated by pressure.

As soon as one end of her pole pokes past the line, it starts dissolving into dust.

She pulls it back!

...Hmmm.

Next, she'll unwind a length of twine made from human hair, add a few fresh hairs and quickly create a little keratin core from her nails, start expanding it to get a good base - then, carefully, poke the twine past the barrier and try to protect it from the field, or at least expand it faster than it can dissolve. 

The whole length falls apart in her hands, collapsing into icky goo. The part over the line, again, dustifies.

"Even a corporeal ward would be risky to test like this..." She glares intently at the space where her twine dissolved. "Senescence, obviously, for the decay - entropy would be the only way to prevent me from overcoming the senescence with wards or vigorous growth..." She scowls. "But how are they being overlaid like this - ?"

"They're coterminous spells," Dulcinea says. "Really coterminous. Positively delicious work."

"...I now have additional questions."

"Isn't that uh impossible? Also how are the walls still standing."