Hi Pierre!
Hi Knut,
I’m afraid this is not easy to achieve. The „Mensurstriche“ in LilyPond are 
technically SpanBars, and they can only be drawn between two bar lines on the 
adjacent staves, and MultiMeasureRests can’t cross barlines. Which incidentally 
also shows that Distler’s concept isn’t flawless…
The easiest solution would be to choose a different way of notation and change defaultBarType:

I came up with the attached partial solution, a layout with shortened
mensuration lines. But two problems remain up to now:

   1: I need a working \bar "|." at the end of the score ( or something that 
looks like it ;-) )
   2: There needs to be some more space between the clefs and the first notes

Cheers,
 Knut
\version "2.19.48" % git 5944d20489bb5b8e4c4907fa3b3bcae9ec275ccb

%
% Engraved 2016-09, Knut Petersen
%

global= {
  \key c \major
  \override NoteHead.style = #'baroque 
  \override Staff.BarLine #'hair-thickness = #0.5
  \set Staff.soloText = #""
  \set Staff.soloIIText = #""
  \set Staff.aDueText = #""
}

sopmus = {
  \global
  \set Staff.midiInstrument = #"pan flute"
  \relative c'' {
    \time 3/4 \tempo \markup { \medium { Gemächlich rasche } \fontsize #-2 \note-by-number #1 #1 #1.0 }
    c2 a2 4 4 g2 f4 c' c c c c d e d2 c4 \breathe f2 c4 es es es f c2 4 4 4 b c a?4. (g8 f 4 a) g2 f1.
    \time 3/4 c'2 ^\markup { \fontsize #-2 \note-by-number #2 #0 #1.0 " = " \fontsize #-2 \note-by-number #2 #0 #1.0 }
    4 f,2 g4 c,2. \breathe c'2 4 f,2 g4 c,2. \breathe c'2 4 f,2 g4 \time 2/4 c,1 \breathe
    g'2 4 4 4 4 4 4 b b g2. \breathe 4 c c \time 3/4 g2 4 2. R2.
    ^\markup { "(immer "\fontsize #-2 \note-by-number #2 #0 #1.0 " = " \fontsize #-2 \note-by-number #2 #0 #1.0 ")        "}
    c2 4 f,2 g4 c,2. c'2 4 f,2 g4 c,2. \breathe f2 g4 c,2. f2 g4 c,2 \breathe c'4 c c a f2 4 \breathe c'2 4 4 4 a
    \shape #'((0.5 . -1.0) (0 . 0.0) (0.0 . 0.0) (0 . 0.0)) Slur f4. (g8 a4 f g c, c'\breve.*3/4 ) c2. 
  }
}

sopal = {
  \global
  \relative c'' {
    c2 a2 4 4 g2 f4 c' c c c c d e d2 c4 f2 c4 es es 
    es f c2 4 4 4 b c a?4. (g8 f 4 a) g2 f2.~2. c'2 4 f,2 g4
    c,2. c'2 4 f,2 g4 c,2. c'2 4 f,2 g4 c,2~2
    g'2 4 4 4 4 4 4 b b g2~4 4 c c g2 4 2. R2.
    c2 4 f,2 g4 c,2. c'2 4 f,2 g4 c,2. f2 g4 c,2. f2 g4 c,2 c'4
    c c a f2 4 c'2 4 4 4 a f4. (g8 a4 f g c, c'\breve.*3/4 ) c2. 
  }
}

sopfoo = {
  \relative a' {
    \override Staff.StaffSymbol.line-count = #0
    \time 3/4 \repeat unfold 15 {s2.} \bar "||" 
    \time 3/4 \repeat unfold  8 {s2.}
    \time 2/4 \repeat unfold 10 {s2}
    \time 3/4 \repeat unfold  2 {s2.} \bar "||" 
    \time 3/4 \repeat unfold 21 {s2.}
  }
}

soplyr = \lyricmode {
  Früh -- ling läßt sein blau -- es Band wie -- der flat -- tern durch die Lüf -- te;
  sü -- ße, wohl -- be -- kann -- te Düf -- te strei -- fen ah -- nungs -- voll __ das "Land. " __
  Veil -- chen träu -- men schon, Veil -- chen träu -- men schon, Veil -- chen träu -- men "schon. " __
  Horch, horch, von fern ein lei -- ser Har -- fen -- "ton, " __ ein lei -- ser Har -- fen -- ton.
  Früh -- ling, ja, du bist's! Früh -- ling, ja, du bist's! Ja, du bist's! Ja, du bist's!
  Dich hab' ich ver -- nom -- men, dich, dich hab' ich ver -- nom -- men!
}

mezmus = {
  \global
  \set Staff.midiInstrument = #"pan flute"
  \relative a' {
    \time 3/4
    R2. R2. R2. r4 a a g4. (a8) b4 a f g2 f r4 b2
    f4 as4 4 4 b f4. 8 4 4 c'2 4 c,2 4 f1. \time 2/4 R2 R2 R2
    R2 R2 f4 4 c' a f4. (g8 a4 f g c, c'1) 2 \breathe 1
    2 1 2 R2*6 \time 3/4 2 4 f,2 g4 c,2. c'2 4 f,2 g4 c,2. \breathe f2 g4 c,2. f2 g4 c,2 \breathe c'4 4 4 a
    f2 f4  c'2 4 4 4 a4 
    << \partcombine
       { \new Voice=up \voiceOne  \relative f' { s1 g4 c, \shape #'((5 . 2.0) (10 . 1.0) (0.0 . -2.0) (0 . -2.0)) Slur f1 (g4 c, a' 1. ) a2. } }
       { \new Voice=down \voiceTwo \relative f' { \shape #'((0 . 3.0) (0 . 3.0) (0.0 . 2.0) (0 . 3.0)) Slur f1 ( s4 s4  s1  s4 c f 1. ) f2.} }
    >>
  }
}

mezal = {
  \global
  \relative a' {
    \time 3/4
    R2. R2. R2. r4 a a g4. (a8) b4 a f g2 f r4 b2
    f4 as4 4 4 b f4. 8 4 4 c'2 4 c,2 4 f2.~2. \time 2/4 R2 R2 R2
    R2 R2 f4 4 c' a f4. (g8 a4 f g c, c'1) 2  1
    2 1 2 R2*6 2 4 f,2 g4 c,2. c'2 4 f,2 g4 c,2. f2 g4 c,2. f2 g4 c,2 c'4 4 4 a
    f2 f4  c'2 4 4 4 a4 f1 ( g4 c,  f1 g4 c, f 1. ) f2.
  }
}


mezfoo = {
  \relative a' {
    \override Staff.StaffSymbol.line-count = #0
    \time 3/4 \repeat unfold 15 {s2.} \bar "||" 
    \time 2/4 \repeat unfold 25 {s2} \bar "||"
    \time 3/4 \repeat unfold 21 {s2.}
  }
}


mezlyr = \lyricmode {
  wie -- der flat -- tern durch die Lüf -- te;
  sü -- ße, wohl -- be -- kann -- te Düf -- te strei -- fen ah -- nungs -- voll das Land. __
  wol -- len bal -- de kom -- men, kom -- men, kom -- men.
  Früh -- ling, ja, du bist's! Früh -- ling, ja, du bist's!
  Ja, du bist's! Ja, du bist's!
  Dich hab' ich ver -- nom -- men, dich, dich hab' ich ver -- nom -- men!
}

#(set-global-staff-size 16)

\paper {
  #(set-paper-size "a4")
  left-margin = 2.5\cm
  line-width = 16\cm
  top-margin = 2\cm
  bottom-margin = 2\cm
  horizontal-shift =0\mm
  %
  #(define page-breaking ly:minimal-breaking)
  ragged-bottom = ##t
  ragged-last-bottom = ##t
  %
  print-page-number = ##f
  annotate-spacing=##f
  
}

\header {
  title = "Er ist's"
  subtitle = "für Frauenchor"
  poet = "Eduard Mörike (1804-1875)"
  composer = "Hugo Distler (1908-1942)"
  opus = "aus opus 19"
  tagline = ##f
}

\score {
  \new ChoirStaff <<
    <<
      \new StaffGroup <<
        \new Staff = sopranos << \new Voice = "sopran" { \sopmus } \new NullVoice = "sopalign" { \sopal } >>
        \new Staff = "foo" \with { \remove "Clef_engraver" \remove "Time_signature_engraver" } << { \sopfoo }  >>
        \new Lyrics \lyricsto sopalign { \soplyr }
      >>
    >>
    <<
      \new StaffGroup <<
        \new Staff = mezzos << \new Voice = "mezzo" { \mezmus }  \new NullVoice = "mezalign" { \mezal } >>
        \new Staff = "bar" \with { \remove "Clef_engraver" \remove "Time_signature_engraver" } <<  { \mezfoo } >>
        \new Lyrics \lyricsto mezalign { \mezlyr }
      >>
    >>
  >>
  \layout {
    indent = 0\cm
    \context {
      \Score
      \remove "Timing_translator"
      \remove "Default_bar_line_engraver"
      \hide BarLine
    }
    \context {
      \Staff
      \consists "Timing_translator"
      \consists "Default_bar_line_engraver"
      \override VerticalAxisGroup #'staff-staff-spacing =
        #'((basic-distance . 0) (minimum-distance . 0) (padding . 1.5) (stretchability . 0))
      \override VerticalAxisGroup #'nonstaff-relatedstaff-spacing =
        #'((basic-distance . 0) (minimum-distance . 0) (padding . 0) (stretchability . 0))
      \override VerticalAxisGroup #'nonstaff-unrelatedstaff-spacing =
        #'((basic-distance . 0) (minimum-distance . 0) (padding . 0) (stretchability . 0))
    }
    \context{
      \Lyrics
      \override LyricText #'font-size = #'+0.0
      \override VerticalAxisGroup #'nonstaff-relatedstaff-spacing =
        #'((basic-distance . 0) (minimum-distance . 0) (padding . 0.0) (stretchability . 0))
      \override VerticalAxisGroup #'nonstaff-nonstaff-spacing =
        #'((basic-distance . 0) (minimum-distance . 0) (padding . 0.0) (stretchability . 0))
      \override VerticalAxisGroup #'nonstaff-unrelatedstaff-spacing =
        #'((basic-distance . 0) (minimum-distance . 0) (padding . 2.0) (stretchability . 0))
    }
  }
}
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