Looks like a common problem.
Perhaps lpub doesn't recognize the unofficial parts path where the lsynth parts are installed. I believe Willy's tutorial recommends the <LDRAWDIR>Unofficial\LSynth directory for these parts, but some programs only look in the standard paths.
What happens if you copy those part files from <LDRAWDIR>Unofficial\LSynth to <LDRAWDIR>Models?
Perhaps lpub doesn't recognize the unofficial parts path where the lsynth parts are installed. I believe Willy's tutorial recommends the <LDRAWDIR>Unofficial\LSynth directory for these parts, but some programs only look in the standard paths.
What happens if you copy those part files from <LDRAWDIR>Unofficial\LSynth to <LDRAWDIR>Models?