Maybe something like:

#! /bin/bash -
pid=${1?Please give a pid}
sep=
while
  [ "$pid" -gt 0 ] &&
    read -r ppid name < <(ps -o ppid= -o args= -p "$pid")
do
  printf "$sep%$((3+${#pid}/2))d%$((4-${#pid}/2))s%s\n" "$pid" "" "$name"
  sep=$'  |\n'
  pid=$ppid
done

Which gives:

$ that-script "$$"
13612  /bin/zsh
  |
 4137  SCREEN screen -xRS main
  |
 4136  screen screen -xRS main
  |
 4130  zsh
  |
 4128  xterm
  |
  1    /sbin/init splash

Maybe something like:

#! /bin/bash -
pid=${1?Please give a pid}
sep=
while
  [ "$pid" -gt 0 ] &&
    read -r ppid name < <(ps -o ppid= -o args= -p "$pid")
do
  printf "$sep%$((3+${#pid}/2))d%$((4-${#pid}/2))s%s\n" "$pid" "" "$name"
  sep=$'  |\n'
  pid=$ppid
done

Which gives:

$ that-script "$$"
13612  /bin/zsh
  |
 4137  SCREEN screen -xRS main
  |
 4136  screen screen -xRS main
  |
 4130  zsh
  |
 4128  xterm
  |
  1    /sbin/init splash

That's a bit sluggish as it runs one ps per process in the ancestry. You can improve it by running ps to retrieve all the information at once and post process it with awk for instance:

#! /bin/sh -
pid=${1?Please give a pid}
ps -Ao pid= -o ppid= -o args= |
  awk -v p="$pid" '
    {
      pid = $1; ppid[pid] = $2
      sub(/([[:space:]]*[[:digit:]]+){2}[[:space:]]*/, "")
      args[pid] = $0
    }
    END {
      while (p) {
        printf "%s%*d%*s%s\n", sep, 3+length(p)/2, p, 4-length(p)/2, "", args[p]
        p = ppid[p]
        sep = "  |\n"
      }
    }'