Is there any chance that LyX in the future will support spell check on fly,
where each misspelled word is underlined with a red line in the editor if
its incorrectly spelled?

I concur that inline spellchecking is not helpful during writing.

Have a look at the User's Guide as well, which explains that LyX simply implements an external program to do the spellchecking. It may happen in the future that LyX will support a program that provides inline spellchecking, but for now it's Aspell for Windows users (and probably most everyone else). Looking at the Aspell documentation (http://aspell.net/), there is no mention of a desire for inline spellchecking, so if you want that you might want to look at another program and work on implementing support for it in LyX.

Dave Hewitt
VIMS, Gloucester Point, VA

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