Steve is right about A. Henry trying a number of ideas on his Jones underlever rifles.
I have three, a .500 hammer, a 577 hammer and a 450 hammerless and they are all different.
That said, I don't see anything on the barrels that acts as a stop for the lever swing.
The design of the lockup is similar to the way a bolt locks into the receiver ring on a bolt action rifle so there is really no possibility of the lever to over travel on closing.
Imagine the opposing bites on the barrel lug are the receiver ring and the Jones lever screws into those lugs as a bolt would turn into a receiver on a bolt action thus drawing the action closed.
The 450 stays open on the tension of the cocker.
The 500 stays open with a little spring latch.
The 577 will flop one way or the other when the action is open as it doesn't have any hold open feature.
All three do have a variation of a stop on the underside of the trigger guard to keep the lever from flopping open when closed.
500
577
450
The 500 has a spring inlet into the lever to mate up with a notch in the underside of the frame where the lever attaches.
It does function as a stop of sorts but it also holds the lever in the open position as well.
The hammerless cocks off of the lever rotation and it looks like the cocking dog is possibly used as a rotation stop as well. Can't get a good picture of that yet