This revolver is a .38 spl version of the Mk III Colt series that included the
.357 Lawman (Trooper Mk III with fixed rear sights). It was produced as issue bait for agencies (LE) that used .38 spl ammunition exclusively. Hence the name, implying city use.
The Trooper/Lawman Mk III revolvers it was scaled down from (shorter cylinder, and engineered to fit that cylinder), are easily among the strongest .357 revolvers ever commercially produced. They are based on a ".41 frame", Colt designated it the "J" frame. Sort of the equivalent of the Smith "L" frame. From a purely safety standpoint, it will eat (if in good condition) an almost unlimited number of +P rounds and simply shrug them off. If you wouldn't hesitate to shoot +P through a Smith Model 10 (and I wouldn't), you shouldn't here either.
From another standpoint, it is one of the vintage Colt revolvers with the shortest production runs. As such few were made and fewer still are available as good condition survivors. Pristine examples are the subject of "collector value" speculation among Colt collectors, rapidly gaining in "collector value".
Shooting any ammo in any gun produces some amount of wear, shooting higher pressure ammo produces more than lower pressure. Depending on the guns current condition and your interest in preserving as speculation on increasing value, you might elect for these reasons not to shoot +P or not shoot at all.
The fact that vintage Colts of certain eras were designed for periodic maintenance that may no longer be available is a much lesser issue with the Mk III and later guns than with previously produced Colts. It is prudent to remember that Mk III and later Colts with frame mounted firing pins should only be dry fired with good quality snap caps as the replacement of these firing pins requires an astronomically expensive piece of equipment found only in the Colt factory and, if you are a pessimist one day will no longer exist at all.
Use snap caps and decide if you have a shooter or a safe queen to one degree or another. If this is a shooter and you accept a lifespan of say only twice as long as your own lifespan, it will eat +P (current SAAMI standards) like candy. I make no claim or comment at all for rounds that exceed current SAAMI standards for +P. You can blow up anything if you try hard enough.
I am a bit green with envy.
Hope this helps.