Yes, Shadow's last hope to prove himself to us is too not fail at Hades...On topic, Let's discuss Lync again...He cried why? Because, he's lost, alone, asking for help from his enemies, and probably heart-broken... All in another dimension.
I think it's because he feels hated by everyone. When he's witht he Vexos he's fine because there are people who don't hate his guts but he's alone in a world full of enemies.