+1 check pressure, per Gerry. So easy to do something that will look really silly down the line... Do the simple stuff first.
Pour boiling
water around the pin area, then ice water, then boiling water, then ice water. Then tap (gently with a brass hammer or a steel hammer on top of a couple sheets of paper) likely spots around that pin to encourage it to behave properly.
That failing, if the thing will go into a freezer, leave it over night, then, immediately, pour boiling water over just the lid like you did before .
While waiting for it to freeze, find a "strap wrench". These consist of a specially shaped handle with a 3/4" - 1" x 12" to 18" strap attached; often people use powdered resin on the strap just baseball pitchers used to do to give improved grip. A chain wrench uses the same idea, but instead of a strap it has a chain - might not want that because it will chew up the aluminum a bit. It may be hard to find a strap wrench with a long
enough strap. Find out how long it needs to be to fit around the edge of the lid, then get some narrow webbing and sew it onto the end of the strap the wrench came with to give you a long enough strap.
There are two ways to use it: Apply the wrench to the lid and hold the pot, or apply the wrench to the pot and hold the lid. In the case of wrench-on-pot, you may want to take a thin (1/8-3/16) piece of
wood and place it under the fulcrum point where the handle contacts the pot. There is a LOT of pressure at that point and it'd
be nice to not puncture the pot. Putting a small piece of sheet metal under that point would also help. The box stores
sell sheet metal as "welding material" and if you're really into it, you can get some 1/8" plate, cut a small piece and then form it into a curve a little tighter than the outside of the pot (hammer it over some kind of form) to spread that load even more.
If you working alone, it will be (has been?) hard to hold the pot really strongly while cranking on the lid - or vise versa. Working on a wood bench that you can screw into can help here. Screw wood blocks into the bench to position either the pot of the lid and catch protrusions to hold it while you twist. That assumes, of
course, that the work bench is "nailed down".
Finally, depending on the damage to the original lid, it's possible it could be welded. There is a break in the skill level of welders. Most "farmyard" welders (like me) don't make it past steel and into the skill level of good aluminum fabrication. So if looking into this, look at what work the person has done on aluminum before deciding.
Breaking an old faithful tool is a real bummer. Best luck.
Rufus