Tie at the beginning of the piece

[Alexandros Droseltis]

Hello!

I try to typeset a fragment-example which does not start at the
beginning of a piece. I want to show, that there are ties that connect
the example to the previous and to the next notes in the piece. That is,
I want something like (this is a minimal example. The ~ causes error, it
is put here to demonstrate what is wanted):

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\version "2.13.1"
\layout {
\context{
\Staff
\remove Time_signature_engraver
}
}
  
\score{
\new Staff\relative c'{
\set Score.currentBarNumber = #29
\bar ""
~ c4 g'2.\laissezVibrer
}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

How could I make the beginning tie appear? How could I make the
laissezVibrer tie longer? 

Using LilyPond 2.13.1.

Thanks for any help!

Alexandros