My understanding is that the "stackless" concept here means that it does not store its execution state in the "C runtime stack" (or Rust, in this case).
So, there is some blob of memory describing that info, managed by Piccolo, rather than it residing on the "real" OS execution stack.
In particular, for call chains like: Lua -> C -> Lua -> C (or so), it is normally hard to save/restore the "C" parts of that chain, since you need to peek into the not-normally-accessible and platform-specific C runtime stack details. I wonder: how are you doing it in your system?
In Piccolo, I imagine it would be easier, since even the "-> C ->" portions of the stack are being managed by Piccolo, not the base C runtime. I don't know what the APIs to access that stuff actually look like, though.
Aside: have you looked at Pluto/Eris for Lua serialization of coroutines?
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EDIT Yes, it seems like the section The "Big Lie" is right up your alley (: