\version "2.19.50"  %% and higher

%% https://lists.gnu.org/archive/html/lilypond-user/2016-12/msg00382.html
%% http://lsr.di.unimi.it/LSR/Item?id=888

#(define space-set
  (list->char-set
    (string->list ".?-;,:„“‚‘«»‹›『』「」“”‘’–— */()[]{}|<>!`~&…†‡")))

#(define (width grob text)
   (let* ((X-extent
           (ly:stencil-extent (grob-interpret-markup grob text) X)))
     (if (interval-empty? X-extent)
         0
         (cdr X-extent))))

#(define (remove-suspended-note-heads stem note-heads)
   (let* ((nc (ly:grob-common-refpoint stem (car note-heads) X))
          (stem-coord
           (ly:grob-relative-coordinate stem stem X))
          (half-stem-thick
           (/ (ly:grob-property stem 'thickness) 2))
          (stem-dir (ly:grob-property stem 'direction)))
     (remove
      (lambda (nh)
        (if (positive? stem-dir)
            (> (ly:grob-relative-coordinate nh nc X)
               stem-coord)
            (< (ly:grob-relative-coordinate nh nc X)
               (- stem-coord half-stem-thick))))
      note-heads)))

#(define (make-center-on-word-callback grob center-on-chords)
   (let* ((text (ly:grob-property-data grob 'text))
          (syllable (markup->string text))
          (word-position
           (if (string-skip syllable space-set)
               (string-skip syllable space-set)
               0))
          (word-end
           (if (string-skip-right syllable space-set)
               (+ (string-skip-right syllable space-set) 1)
               (string-length syllable)))
          (preword (substring syllable 0 word-position))
          (word (substring syllable word-position word-end))
          (preword-width (width grob preword))
          (word-width (width grob (if (string-null? syllable) text word)))
          (note-column (ly:grob-parent grob X))
          (stem (ly:grob-object note-column 'stem))
          (stem-dir (ly:grob-property stem 'direction))
          (sys (ly:grob-system grob))
          (nh-ls
           (if (ly:grob-array? (ly:grob-object note-column 'note-heads))
               (ly:grob-array->list (ly:grob-object note-column 'note-heads))
               '()))
          (full-column-width
           (interval-length (ly:relative-group-extent nh-ls note-column X)))
          (note-column-width
           (interval-length
            (ly:relative-group-extent
             (remove-suspended-note-heads stem nh-ls) note-column X))))
     (-
      (*
       (/ (if center-on-chords
              (if (positive? stem-dir)
                  (- full-column-width word-width)
                  (- (* 2 note-column-width) full-column-width word-width))
              (- note-column-width word-width))
         2)
       (1+ (ly:grob-property-data grob 'self-alignment-X)))
      preword-width)))

#(define (center-on-word grob) (make-center-on-word-callback grob #f))
#(define (center-on-word-on-chords grob) (make-center-on-word-callback grob #t))

\layout {
  \context {
    \Lyrics
    \override LyricText #'X-offset = #center-on-word-on-chords
  }
}