Hi Orm,
Use voices. Here's a rough outline answer sketched out quickly, without seeing the publication you refer to.
Basically you can only tie across notes in the same voice, so that clues you in as to the way to set such music.
Andrew
== snip
\score {
\new Staff \with { tieWaitForNote = ##t } {
\clef "bass"
\key e \major
\time 3/8
{
<<
{
\voiceOne
e'4. ~ 4 s8 \stemDown
}
\new Voice
{
\voiceTwo
s4 b8 ^~ |
\stemUp b4 \stemDown b,8 ^~ |
\stemUp b,4. ^~ |
b,4. |
}
\new Voice
{
\voiceThree
\shiftOff
s4. |
\once \override NoteColumn.ignore-collision = ##t
e4. ^~ |
e4. |
}
\new Voice
{
\stemDown
s4. |
e4 s8 |
e,4 b,,8 ^~ |
b,,4. |
}
>>
}
}
}
== snip