How does preserved lemons salt soultion form a gel?

It is possible that you have precipitated the proteins to some extent by the salt concentration (known in biological fields as "salting out"), which might produce a gel-like blob, just like cooking egg-white does.

You can indeed also precipitate proteins with sugars (e.g. here), though it is more commonly used for extraction of organic acids (e.g. decenoic acid) from fruits etc, it will take quite a bit of experimentation to do this as it usually requires a very high concentration of sugar and quite a high concentration of protein too. You are more likely to get the pectin (which is a polysaccharide) to work, before you get the proteins to precipitate in a sugar solution.

Three other possibilities are (I think #3 is most likely):

1. salt-tolerant mucilage-producing bacteria. I don't know of a species, but it's possible.

2. pectinase happened. Pectin is activated with heat as you said. But pectin can be enzymatically broken down into simple sugars and acids. Over time, as water evaporated through the corroded seal, the sugars present in the lemon and from the broken down pectin would concentrate along with the various acids to form a thick syrup which might appear as a gel.

3. low-methoxyl pectin which can set at room temperature and is present in citrus peels. It requires a little sugar and calcium to set... Both of which lemons do possess in small quantities. My personal guess is that over time as water evaporated and cell walls broke down releasing pectin, the sugars and calcium naturally present in the lemons reached concentrations that allowed the low methoxyl pectin to set properly.

Having said all that, it's impossible to know for sure what happened to your nightmare lemons, but as far as raw marmalade goes, it's 100% possible if you use additional pectin. You can buy the no-cook type in most US grocery stores in the canning section (unless that's just a southern thing? I don't know.)

But the pectin present in the lemon peel and cell walls won't come out and become useable unless those cells are broken down, and the usual ways for that to happen are heat (which defeats your purpose) or bacterial action/decomposition (I don't know how to do it safely, so just say no, kids). I suppose you could try puree-ing the living daylights out of a lemon and see if you can get enough pectin to come out mechanically that way, but... I have no idea if that would work and I personally doubt it.