Chances are the issue is with resistance of the driven disc sliding on the hex shaft.
With the mower off, unclip the short arm from the end of the long shifter arm. Remove the clip and the short arm.
A spring holds the driven disc against the drive disc. Disconnect that spring.
Does the driven disc slide freely along the length of the hex shaft? If not, remove the driven disc and clean the parts. Same also for the shaft in the bracket bore.
IMO, lubrication will just attract dirt, making the problem recur quickly. If lube is used, such as WD-40, for a cleaning agent, then wipe it away at assembly. Mine works fine w/ keeping the parts clean w/o lube.