They will have some backbone in it, plus most usually a rib bone. They are usually cut to have 1 rib bone per chop, though occasionally a chop will be missing its rib bone altogether.
The meat in it is from the rib eye section, and very tender, but with no tenderloin, as that is in lamb loin chops.
The butcher may scrape away meat from the end of the rib bone to expose the bone, making it “Frenched” for a more decorative presentation (though some people object to the loss of meat, especially given how small lamb chops are to start with.)This is called a French Lamb Chop or a Frenched Lamb Chop. Though it doesn’t specify rib, rib is inferred because the loin chops, with their T-Bone, can’t be Frenched in this manner.
If a Lamb Rib Chop is cut more thickly, there may be two rib bones. This is called a “Double Cut Lamb Rib Chop.” It will be about 2 inches (5 cm) thick.
If cut more thickly even yet, there may be three rib bones. This is called a “Triple Cut Lamb Rib Chop.”
The outer edge of the chop is covered in a layer of fat, giving them more fat than loin chops, so they will cook up moister and with more flavour. The fell on top of the fat is usually removed.
For frying, broiling (aka grilling in the UK), grilling (aka BBQ outside the US) or roasting.