Babel is a package added onto LaTeX. It essentially consists of stylesheets to allow documents to be formatted in a manner appropriate to any language's conventions.

Using babel for polytonic greek consists of adding the following commands to the preamble of your LaTeX document:

\usepackage[polutoniko, english]{babel}

This is done by selecting LyX->Layout->Document->Preamble and entering the above text.

The above is correct for LaTeX2e, and differs from the older command used with LaTeX2.09

To select a passage of text within the body to be formatted as Greek it is best to use:

\foreignlanguage{greek}{passage to format}

To view the options useable with the babel package an xdvi /usr/share/texmf/doc/generic/babel/user.dvi will display the full manual page. It also explains the key-stroke combinations necessary to obtain macrons, rough/heavy breathing and iota-subscripts.

\usepackage[or]{teubner}
in the preamble should allow the use of all the teubner style stuff.

Gotchas.