LyX features important for me:
* LyX don't "mess up" formatting. (indents, blank lines, lists,...) When
writing some pages for my students, I don't really need to check output
because it all just works. Everytime. I can also write down what
happens at a meeting in real time, and mail out a PDF as the meeting
ends. LyX never put a heading on the bottom of a page either. Cross
references and TOC is always correct. (Apparently, a more expensive word
processor struggles with just that. Users need to 'update the TOC' or
whatever?)
* LyX can typeset straight margins with good hyphenation, without
getting excessively long spaces between words. This alone is a good
reason for using LyX. Ragged-right looks unprofessional, and so does
lines with excessive interword space.
* LyX is very good for multi-file documents! Example: I have a file with
a chapter describing "network firewalls using linux". This is included
into a larger document about network security. It is also used in
another document about securing linux servers. These two documents have
different length and different number of chapters. So the firewall
chapter may be chapter 3 on page 14 in one case, and it may be chapter 2
on page 7 in the other case. There are no problems with this. The TOC,
the page & figure numbers, everything works in both cases! So if I add
another section to my "firewall" document, there is only one place to
edit. There is no effort keeping the other two documents 'in sync';
because there are no copies to synchronize.
* Another multi-file case: I teach programming. So I need source code
examples. I can embed references to source code files in LyX. Again,
there is only one place to edit - the source code file. When LyX
produces a PDF, it reads the source code files and typesets it -
complete with syntax highlighting! And no effort keeping the compilable
source code 'in sync' with the document. No code is copied into LyX,
only a reference to the filename.
* LyX can use just about any LaTeX feature. But I don't need to use
LaTeX commands for everyday writing, it is as easy as any other word
processor.
* LyX supports my language well, and lots of others too. Both the user
interface, hyphenation and spellchecking. Commercial word processors
have less support for 'small' languages.
* LyX does presentations as well as text document; so I don't need
powerpoint. I wouldn't know how to get something like a tikz animation
in powerpoint anyway.
Other cool features:
* Excellent math support. Any formula of interest can be written in LyX.
It won't be hard, and it will look good. Thanks to the LaTeX backend, of
course. Lyx will also interface with math software; press a button and
it will do difficult integrals for you, by asking maxima or mathematica.
* LyX cooperates with Lilypond, so you can have both music and text set
nicely.