(Fellow semi-beginner's response:)
I tried this with the different ways of viewing text
available to  me on the mac with no problem. 
I notice the LyX manual says, discussing the
text styles dialogue, (3.6.4):

Color: You can adjust the color of the
 text with this control. Notice that not all dvi-viewers
 are are able to display colors. ...

Then googling Yap color text I promptly got
http://www.gnustep.it/marko/GPSText/index.html
saying:

Getting colored output:
Set "PostScript Device" to "24 bit color" 
for color previews; use the style sheet "color" 
to get colored a2ps output. 
This only works if the color style sheet
 is installed on your system 
("/usr/bin/a2ps --list=style-sheets").
Note that mutally contradictory options 
to a2ps may cancel each other out.

So it looks like its to do with Yap, which is 
bundled with Miktex. It would probably be 
easiest to set something else as a viewer, 
through the general LyX preferences:
Preferences --> File Formats --> DVI
then look whats listed as the viewer - and
try to change it.  I don't know what else
you may have to view it, but there is 
plenty about this sort of thing if you 
search these posts, for example. 





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