Due to reasons outside the scope of this forum, my Traeger Jr. has sat unused for too long (outside, but with the factory cover on it). I finally pulled the cover off this weekend and started cleaning it up and getting it ready for use again. Unfortunately, the lid hinges were rusty and one of them broke before before the penetrating oil could completely work its magic.

I finished cleaning the smoker and did an initial cook (it was only hot dogs, but it was still something), but it is a little difficult keeping the lid open when only one hinge works. I'm looking for suggestions on making the lid more functional (buying a new smoker is not in the budget this year :-). My current thoughts are to cut off the existing hinges and bolt on two new stainless steel hinges. I'll need to give some thought to how the new hinges get mounted, so that I don't end up with too big of an air leak.

Anyone have any different thoughts? Thanks.

1st off, welcome to the site. 

2nd, I wouldn't worry about the hinges if smoke escaping is a concern. Yer gonna get that out the back vents and the grease drain hole anyway. Smoke will take the route of least resistance and a few ill placed holes won't add up to spit.

What I would recommend is replacing both hinges with the same. No OEM combined with an aftermarket version.
In doing so, you 'may' have a potential issue that's easily correctable as the hinges are the same. Mix and max could be much more difficult. 

 Another "Welcome", from Canada.

What exactly broke re: the hinge?  If memory serves me well, the hinges are welded to the lid and bolted to the body using machine screws and rivnuts. 

One of the hinges broke.

The hinges are welded to the lid and bolted to the body. Replacing both hinges looks like it would be best. I'm thinking about cutting off the working hinge and bolting two new hinges right next to the old ones (using stainless hardware). It will probably result in a larger gap between the lid and the body, but I expect there are ways I can mitigate that, if I find it annoying.

One of the hinges broke.

The hinges are welded to the lid and bolted to the body. Replacing both hinges looks like it would be best. I'm thinking about cutting off the working hinge and bolting two new hinges right next to the old ones (using stainless hardware). It will probably result in a larger gap between the lid and the body, but I expect there are ways I can mitigate that, if I find it annoying.

Sounds good. Use the original hinges to position the lid while drilling the holes for the new hinges... I used to keep my hinges lightly lubed with synthetic motor oil, mostly as I don't like squeaks. It reduces wear as well.