I commited a patch to finish the support for environment nesting in tex2lyx. I hope it works now, because the code is really beginning to look ugly...
As far as I can see, the tutorial (which is a simple thing, actually) can now be exported to latex and re-imported nearly identically. I would be interested by any reports on things that still don't work in the document-structure department.
Of course there are a lot of things not supported by tex2lyx, but this was an important (and painful) step.
JMarc