Let's nail down some terminology before we get too deep into techniques, just to make sure we're talking about the same thing.
When I say, "barbecue," I usually mean using fairly low indirect heat, 300F and below, along with wood smoke from burning hardwood in a (mostly) closed pit. These pits are often called "smokers." But sometimes I mean, "open pit," which exposes the meat to an open fire, but at enough distance that most of the cooking is via convection rather than radiant heat. Temperature at grill height typically runs in the mid 300s. When versions of these are sold, sometimes they're called "Santa Maria style grills."
When I say, "high heat indirect," I mean using fairly high heat, 300F and below, using gas, hardwood or charcoal for fuel and possibly but not necessarily using hardwood for smoke. A Weber Kettle excels at this kind of cooking, so do many gas grills.
When I say, "grilling," I mean cooking the meat on a grate directly over a heat source mostly with radiant heat. You can use any normal backyard gas or charcoal grill for this.
Let's move on to the raw hunk of meat...
If you cut it into "chops," it's no longer a rack and the chops aren't "rack chops," they're "rib chops." They make excellent grilling. The best way to do them is over a very hot temperature for as short a time as possible to get them to rare, then let them rest a bit and coast into medium rare.
A whole rack is roughly triangular. The bottom is protected by "feather bones." The back is protected by rib bones. The front is covered by fat called "fell." Sometimes a narrow strip of meat runs through the fell. If the rack is untrimmed, the fell will extend all the way up the front of the rib bones. Sometimes the fell is trimmed so part of the bones are exposed.
If you trim the meat off the rib bones down to the "eye" or "mignon" and clean the areas between the bones the rack is said to be "Frenched." If you remove the fell so the face of the mignon is exposed, the rack is "cleaned," or "trimmed," or "cleaned and trimmed." Most lamb fat, including the fell is very heavy and unpalatable. It's considered good practice to trim lamb very closely. This usually means losing the the little strip of meat above the top of the front of the rib bones which is delicious. Traumatic, no?
If the cook decides to protect the meat, sometimes other fats like bacon are layered on the exposed face ("barding") or sometimes other coatings are used, bread crumbs for instance.
There are a number of good ways to cook a rack whether it is left untrimmed or cleaned and Frenched or somewhere in between. I favor the open pit method, or high heat indirect grilling -- with some wood smoke involved. Lamb responds especially well to oak, mesquite, grape cuttings and citrus. Hickory is just okay, and alder a little mild.
I usually clean the rack, but don't french the bones as the meat, fat and connective tissue between them is quite tasty. Since outdoor cooking usually precedes informal dining, the messiness of gnawing the great stuff off the bones is not a problem.
I slather the face of the trimmed rack with a mix of mayonnaise and dijon and season very heavily with a rub including plenty of fresh herbs. Then use either a Santa Maria style grill for open pit, or a gas fired offset for high-heat indirect -- probably neither is available to you.
If you do have a Weber Kettle type charcoal or a gas propane grill with a lid, I recommend cooking the rack over indirect heat at about 350F. That 350F is the actual temperature at grill height next to the meat -- not the reading of the hood thermometer which has nothing to do with anything.
If you want to get more specific, let me know a little more about your 'Q, and we can work something out for you. I've got a great recipe for a Provencal lamb with an olive cream sauce that I've adapted for outdoor cooking which may be more ambitious than you want to go. But you get the idea -- your options run from the simple to the haute.
Hope this gives you some ideas,