left outer join in lambda/method syntax in Linq

You're close. The following will select PID, CID and Text for each child, and PID, CID = -1 and Text = "[[Empty]]" for each parent with no children:

var source = lParent.GroupJoin(
    lChild,
    p => p.PID,
    c => c.PID,
    (p, g) => g
        .Select(c => new { PID = p.PID, CID = c.CID, Text = c.Text })
        .DefaultIfEmpty(new { PID = p.PID, CID = -1, Text = "[[Empty]]" }))
    .SelectMany(g => g);

from p in Parent
join c in Child on p.PID equals c.PID into g
from c in g.DefaultIfEmpty()
select new 
{
   p.PID,
   CID = c != null ? (int?)c.CID : null, // Could be null
   Text = c != null ? c.Text : "[[Empty]]"
}

With lambda:

class ChildResult
{
   public int PID { get; set; }
   public int? CID { get; set; }
   public string Text { get; set; }
}

lParent.SelectMany(p => p.Childs.Any() ?
  p.Childs.Select(c => new ChildResult() { PID = c.PID, CID = c.CID, Text = c.Text }) :
  new [] { new ChildResult() { PID = p.PID, CID = null, Text = "[[Empty]]" } } );