I have built an example prototype widget that tries to combine LyX and
Jupyter Notebook together.

Is it implemented via QtWebEngine. Basically, by embedding a mini webpage
browser inside LyX.

A screenshot is here:
https://github.com/jupyter/notebook/issues/1604#issuecomment-507746234

A bidirectional communication between LyX and Jupyter Notebook could be
implemented via this browser. With the help of jupyter lab, we can get
cross platform terminal for free.

Would this be something worth further pursuing down the road?

Using Web, a lot could be implemented. Especially, Qt 5.13 introduces Web
Assembly. With the help of that, LyX could have it OverLeaf counter part
with stronger abilities!

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