Awww, I love that picture!
Yep, I notice a horse's eyes right away. If they're soft, kind, and inquisitive, I know the animal most likely has a good heart and lovely disposition.
The first time I saw JJ, his trainer pulled him out of his stall and he promptly cocked one back leg, got comfy, and half closed his eyes. I told her, "My goodness, what a holy terror he is!" We both laughed.
JJ likes nothing more than to be the center of attention. He'll even chase away my grey Arab gelding if he thinks Casper is getting more than his fair share of scritches and love.
I'm sure Lance will find the right home, especially since you're retraining him. JJ was just off the track when I brought him home, although it didn't take long to retrain him. He likes being active, and enjoys his under saddle time. Lance appears to be the same way.