When Jane is sitting in the park feeding obvious misinformation to Lisbon, that is when he works out that pigeons are a clue.  He's sitting there thinking about his own happy memory when his mind wonders to Lisbon's happy memory of her mother feeding pigeons (http://www.youtube.com/watch?v=YRtjwu2xg1o).  He notices the woman (who looks a lot like Brett Partridge) feeding the pigeons and it dawns on him that the pigeons are a clue!