First, they've got to have a thick skin. You don't have to tolerate abuse, but you do need to understand that when good lineman get on you, it's usually because they care about you and want you to succeed. If you're getting the silent treatment, that's when you should really worry.
Second, they are competitive. They want to be better than the next guy. Third, they show initiative. Even when there is downtime, they find something productive to do. They ask questions, speak up when they see something unsafe and keep themselves physically and mentally fit.
And finally, they understand that being a great lineman also means having a healthy balance between work and home.