Does leaving the lid on make a difference to whether the meat in a soup softens/cook properly?
The only thing that gets the connective tissue in tough cuts to loosen is heat. With the lid on, you've got more insulation. I'd bet you a shiny nickle that the meat towards the bottom of the pot was a touch more cooked than the meat at the top of the pot— you're losing a lot of heat where all of that liquid is hitting room-temperature air. With my immersion circulators, for example, I can't keep the water bath much above 70c without covering them, but the second I cover it, the temperature shoots right up. So sure, the lid likely made it cook a little more quickly and evenly. That said, allowing your cooking liquid to evaporate and intensify as you stew your meat can be a good thing too.