I found the solution. Of course it was already (somewhere) in the
manual.
http://lilypond.org/doc/v1.8/Documentation/user/out-www/lilypond/Invoking-lilypond-book.html#Invoking%20lilypond-book
says:
"
For printing the LaTeX document, you will need to use dvips. For
producing PS with scalable fonts,
After finding the file missfont.log created by dvips, I'm one step
closer to the problem. Apparently when I run dvips after running
lilypond-book on a tex file it uses other fonts (directory?) than when
it's invoked by lilypond itself on a plain .ly file, resulting in
garbage output produced by dvi
