Member dfariswheel has a multitude of threads and posts on revolver inspection, timing, lockup, cleaning and other extremely useful information. AIA is "The Searcher" and can find all of them. I can't find anything, including my coffee cup this morning. Bad day at Black Rock. Search for revolver inspection, endshake, cylinder movement and you may run into a post or thread by dfariswheel that will go into great detail on things to check/inspect/correct.
All the Vspring/rebound lever action Colts that I ever had and have,do not have ANY rotational movement in the cylinder when trigger is held back. THe second stage or lower "finger" of the "hand" pushes the rachet and cylinder so that the notch in the cylinder is tight against the side of the bolt face. So there really should not be ANY movement in that mode.
Fore and aft movement is variously called end play or end shake. The factory spec for most Colt DA revolvers is .003" maximum. This can be measured by first holding the cylinder forward or rearward and measuring barrel to cylinder clearance with a feeler gauge and then measuring the clearance with the cylinder held in the other direction. The difference in measurements is the end play. A common cause of excessive end play is the shortening of the cylinder collar from wear and impact, although other things such as frame stretching and ratchet face wear can happen. The usual factory fix is to stretch the collar (one time) and refit the cylinder. Depending on the actual cause, this can also require refitting the barrel so final barrel cylinder clearance is correct.
And note that unlike many other brands of revolvers, Colt's CANNOT have washers dropped into the cylinder shaft hole or have the crane shaft stretched to correct end shake.
If you're Colt is over 0.003" it needs a trip back to Colt.
Let it go any farther and the gun can be damaged.