Am 16.09.2015 um 11:33 schrieb Erich Neuwirth:
%% Can I get the beams of the triplets between the staves
%% such that the stems are up up down?

Stem directions can be manually changed by the commands \stemDown, \stemUp, \stemNeutral and by \voiceOne, \voiceTwo, \voiceThree, \voiceFour, \oneVoice. The latter also change tie and dot directions and some other things. You can just use “\once \stemUp” in front of your “g'”s.

Slightly offtopic: It’s easier to use the two voices for the whole measure (or even longer parts of music), you don’t need a << \\ >> for every note:
%%%%%%%%
lower = \relative c' {
  \clef bass
  \key c \major
  \time 2/4
  <<
    {
      \tuplet 3/2 {b8 c  \change Staff = "upper" \once \stemDown g'}
      \change Staff = "lower"
      \tuplet 3/2 {g,8 c \change Staff = "upper" \once \stemDown g'}
      \change Staff = "lower"
    }
    \\
    {
      g,4 d
    }
  >>
}
%%%%%%%%

%% The second triplet wrongli incorporates the quarternote d,4
%% and the beam also shuld be above the first two notes,]
%% like in the first triplet

It’s not really LilyPond’s fault: << music othermusic >> tries to make chords from music and othermusic, while << music \\ othermusic >> makes true polyphony. So just add \\ like you did in the first half of the measure.

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