I've shod horses that were leaners and it's pretty hard to know why without seeing them. Sometimes a past injury will cause them discomfort and you just have to work around a bit to find a position where they relax. It may put you in a position that is not too comfortable, but sure beats the heck out of trying to hold one up. I used to shoe for several ranches and most of them still had their old barns with a wooden floor. Occasionally, I'd shoe one inside. Seems like the difference in footing helped for some. I've also had some success with tying a foot up. Anything you do like that, using a twitch, etc. , depends on the horse and its disposition.
I totally agree with JHawes and keeping them quiet. On many occasions, I had owners remark that I sure had fewer problems than the last guy that shod their horse. Sometimes, the old pony just needs to know you didn't show up just to whip on him. The jobs I liked best were the ones where you got the call, did the work and got the check in the mail. The old saying, "When they showed up to help, it was like having two good hands walk off," comes to mind with some owners.
Is this new one a mule? I don't have a lot of experience with mules, but they can be a very cagey animal. My ex-father in law cowboyed and guided hunters all over the Wind River Mountains for years. He had quite a string of mules. By the time I met him, he was pretty much down to cowboying in the summer and reading Louis L'Amour books in the winter. I wish I had known him in his younger days. A wealth of information and experience died with him.
One a final note to my windy reply - I've told my kids that I'm old enough to assume an advisory role now. Got any younger guys around that neck of the woods? I'd put them to work.