LyX is the fastest interface I have come across for mathematical syntax, due to the great foundations and comprehensive input mapping. It would be lovely to be able to use generally as a notebook, especially if there were some upgrades to the rudimentary CAS (computer algebra system) support included up to V2.
One feature fundamental to this goal is the parsing of respective CAS languages, obviously, in particular multi-line expressions. In the case of Maxima, I experimented with LyX -> LaTeX -> Maxima conversion in manual steps, playing with SnuggleTeX, but apart from requiring generous amounts of scripting being a java library this is not the most straightforward way to interact with LyX or Maxima.
If someone were to start a project to improve on LyX's CAS integration this would interest me greatly and I would look forward to contributing. The idea of ultimately converging to plain-readable interactive scientific documents together with projects like Sage to me is truly exciting, and I hope that LyX's interface can be part of it.