Lemon juice as a natural preservative for soups
Anything that will keep bacteria and other spoilage microorganisms from growing will extend shelf life.  Acidity and salt are the most common historical preservatives, since they create inhospitable environments for many microorganisms (or only allow the growth of ones that are less harmful).  In high concentrations, sugar can also function in this way, as in jams or jellies (though this is probably not applicable to soups).  Unfortunately, any soup with enough salt and/or acidity to stop bacterial growth entirely will probably be unpalatable.

That said, lemon juice is highly acidic, so it's likely that it could prevent spoilage a little longer than in soups without it.  However, unless you're adding a lot of lemon juice, chances are this effect will not be long enough to call it a "preservative" -- but it might make your soup last a day or two longer in the fridge.  A fairly acidic soup using things like tomatoes, lemon juice, vinegar, etc. will generally last a little longer than a similar one without those ingredients.

Nevertheless, the normal storage recommendations for soup should still be observed.  Soup in general is very perishable.  Stocks and broths are a near ideal growth medium for any bacteria that might contaminate them, and various ingredients in soups could contain spore-forming microorganisms that are not completely killed during cooking.  More importantly, not all spoilage -- even that from dangerous bacterias -- produces odors or molds that could be easily spotted.  Thus, while adding more acid to soup probably makes it safer a little longer, I still wouldn't depend on it to last more than a few days even using proper cooling procedures and stored under proper refrigeration.

As for cabbage, I'm not aware of any significant anti-microbial properties.  It's possible that soups which contain more vegetable matter (like cabbage) will also contain less meat and other ingredients prone to fast spoilage, but the cabbage by itself isn't likely to have a significant effect.