Generically speaking meat that is appropriate for a braise is tougher and has connective tissue that can be turned to gelatin by the long slow cooking process. As you've noted, meat that is tender can be "cooked to death" using that same method, so I would, generally, recommend against using a braise.
However, a stove top braise can go quickly without ruining the meat, if you keep it short and treat the braising liquid as more of a sauce than anything else. I would suggest that you brown each side of your lamb chops, then add all your other ingredients. Depending on the amount of liquid your original recipe calls for, you might want to cut back. I wouldn't want more than 1/2 cup or so of liquid. "Braise" covered on the top of the stove for 1/2 hour, never going past a simmer. Pull out the chops and cover, while you reduce the braising liquid to make it more sauce-like, then spoon onto the chops.
Note that you won't have the long time to meld flavors, and if there are big chunks of garlic or onions, they won't be a sweet as in the longer braise. But you should get a serviceable dish.
Always let a braise cool in its liquid to prevent drying out. As the meat cools, the fibers relax, allowing the juices to be pulled back into the meat. Imagine squeezing out a sponge (heating the meat), and then releasing the sponge in water (cooling the meat). (People on this forum have disagreed with this statement before, but I stand by it.)
Although allowing the meat to cool for 30 minutes or so will yield fantastic results, if you are an overachiever, putting your meat in the refrigerator overnight will increase the effect. After the meat is cold, it will become more solid, making it easier to remove bones, slice the meat, and skim the fat.
However, I never do this because I am impatient, I kind of like the mouth feel of a little bit of fat, and the results are very good without it. I suggest leaving the refrigerator for the leftovers, which will be wonderful.
BTW, pay less attention to the time, and more attention to the state of the meat. 4 hours may be too much, or two little. The best judge of whether the meat is ready or not, is to taste it. This points to one more advantage of the overnight refrigeration, controlling exactly when you want your food to be ready the next day.
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One potential downside to this method is that with a thick coat of flour, you're mostly browning the flour, not the meat, and thus possibly creating different flavor compounds than if you were searing the meat directly. Maillard reactions are complicated stuff. If you're doing this, you should probably shake off excess flour to leave a very thin layer so that you still get browning on the meat itself.
The related problem is that you're less able to accurately measure the amount of flour, less able to make sure it's easily browned, and thus less able to control the overall balance of thickening power and flavor it contributes. Roux (flour cooked in oil as a base for sauces) gains additional flavor, but loses some of its thickening ability as it cooks. You could monitor this over the surface of your meat, but that goes against the typical wisdom of not moving meat around the pan as it browns - that is, you can't see how browned the floury surface is getting when it's face-down.
Personally, I'd prefer tighter control over both of these processes over the convenience gained by browning the meat and flour together. You can easily brown the meat, remove it from the pan, then add the flour and some additional oil to create a separate roux without losing much time. A slurry will work too, but takes plenty of cooking before it loses its raw, grainy flavor.