Will this work without the ring? Can I add a ring and make my pin lock just a bit easier to use?
I'm from Brasil, and the kegs found here always came from coca-cola, and have the pin-lock as standard. Here you can't find the ball lock ones. All the kegs I've ever seen here has this kind of lid, or something a little different:
This ones uses the kind of pressure relief valve you cited in brewchez' answer, and is always screwed from the bottom of the lid. This kind of valves are not replaceble by the ball lock lid type, and cannot be pushed or pulled to release the pressure. The only thing this prv can do is prevent your keg to explode. It will release the pressure beyond a limit (cornelius keg say it hold 130 psi, but I don't think the old ones find here will hold that). Once it has make its job, its done. You will need to replace it to use the lid again.
I believe that your lid is like that.
With this kind of keg set you will need to release the pressure by the gas in post poppet. Just push the poppet with a screwdriver or something like that.
Or you can just buy a new lid with a gas releaser valve. But if you don't want buy nothing, I recommend to fill your keg with water before use it with beer and put CO2 in just like as you would do when force carbonate in fast way. Set to ~30 psi and lay the keg and shake it for about 10 minutes. If it holds that, so your ok to go. If you don't do that before, you can end with your beer leaving your keg by this valve like a geyser. It happened to me, and I think that check it before worth the effort. Good luck.
EDIT: it seems that the valve doesn't need to be replaced after use. Check this question: Do pin lock static relief valves need to be replaced after activation?
I have never seen one like that. It doesn't look like a pull release at all. It looks like its more of a press to release. So in that case a pull ring wouldn't work.
I'll edit this if information changes.
EDIT: This looks like an adulterated lid to me for some reason. Normally the PRV screws in from the top and looks like this: PRV from Midwest
If you get one hopefully you can simple remove that yellow thing and screw a proper PRV into the top. Otherwise I think you are stuck. Buy a whole new lid is the best bet, one with a proper PRV.