I'm trying to figure out how the books draw a box perhaps with different background around a digression/example? Preferably how this would be accomplished in lyx, but latex solution would be welcomed as well :D
The color package should allow you to use the \colorbox command.
Examples (cited from this page, where you will find more details):
\colorbox{red}{Black text on red background}
\fcolorbox{blue}{red}%
{Black text, red background, blue frame}
If you need just a border and no background color, the built-in \fbox{text} command should do fine.