This is not unusual. If a horse does not lope early on and they get you to pull them a few times, they will develop a real 'thing' about going into a lope. They make a big-time stand against loping or they buck your a$$ off when they do lope. I have seen horses go to extraordinary ends to avoid it once they have made a thing out of it.
You have a couple of viable options. Get someone that is not afraid of having a horse buck. We have a neighbor that is a really good 'cowboy'. He just makes them go on and they get right over it. But, the owner still has to be assertive enough for the horse to take them seriously when they get back on the horse.
There is another little 'gizmo' that works very well for horses that are not complete broncs. I have been in bad enough physical shape for several years that I could not let a horse buck at all. I have always tried to keep every horse from bucking for several decades, but it is not always a possibility, especially if someone has already let one buck.
This little gizmo is very effective for keeping a horse's head up. It is an 8 foot long little 1/4 inch nylon cord that I use for an 'overcheck' type of thing. I tie a bowline knot to the snaffle bit on the right side of the horse's head. Then, I run it through the top ring on a nylon halter, go behind the saddle horn, back through the top ring on the left side of the halter and tie it to the left ring of the snaffle bit just above and in front of where the headstall attaches. Then I make a double half hitch at the saddle horse and put it over the horn so that it cannot come off. If you adjust it so that the horse cannot lower its head below where it is level with the saddle horn, the horse cannot buck hard and cannot lower its head.
This is very effective in keeping a horse from lowering its head and very few horses can buck effectively with their head up. I have used this method on colts for almost 50 years. I even use it when I ground drive one only with a little more slack in it. It does not make a horse rear or do anything wrong and it can make cold-backed horses and horses that want to 'stall out' and threaten to buck keep their heads up and give you a chance to make them ride tight.
Most horses get like this because their riders fear being bucked off and pull them up as soon as they get a little hump in their back and threaten to buck. These horses get rewarded for doing the wrong thing and they get this behavior very entrenched in their minds.
Whether you are using a 'overcheck' or not, the most effective way I have found to teach a reluctant 'sticky' horse to go forward in a lope after it has already gotten spoiled is to spank it with an 'over and under' technique using the ends of a pair of long, heavy harness leather reins. The horse should be out in an open area that is big enough for the horse to go on for a ways at a lope. I do not like moving a horse out in a round pen. I think it is a terrible place to correct this problem. I frequently take them out to the National Recreation Area south of my place where there is a trail that goes on for five or six miles. I can get any of them to move on out there.
You are not going to hurt a horse when you spank its butt. If you do not have the resolve or the 'cahones' to actually make a horse go on, then don't start it and fail again. Get someone else to fix your problem for you or sell the horse to someone that will make it mind. Never try to just 'peck' on one. They get worse. If you ask them, you just HAVE to make them go. I have seen some pretty obnoxious spoiled horses that not only did not want to lope out but would actually stop and start backing up when you tried to force them to. A good spanking with a pair of harness leather reins won out over all of them. Warm that butt up and they will look for someplace to go.
This is just another one of the many problems that get established in horses when they are not made to mind in the first place. You just should not ask a horse to do anything that you are not prepared for and able to make happen. Every time you 'back off' and do not complete a task asked of a horse, it gets a little more spoiled and a little more determined that it does not have to do anything you ask. If the horse wins enough times, it will simply not do anything you want. Instead of gaining respect for you, it will hold you in complete contempt. Refusing to lope is one of the many things they quickly learn to do.