Substitute for onion sweetness?

You might try carrot. It is a common ingredient, often used in Italian cuisine, for example, to counteract the acidity in tomatoes, when making a sauce. In my example it is grated, then simmered with the sauce. It won't break down as much as onion, but could add the subtle sweetness that you are missing, and if finely grated, I doubt you would notice it texturally.

For thickening you have many options, I'd suggest rather than cornstarch that you make a roux of flour and butter as that will give the opportunity for adding flavor as well. For stews I like to make a medium roux in larger quantities than I may need and then set it aside, adding it later to the right consistency towards the end of the cooking process. The browning of the roux adds some of the flavor you lose by removing the onion.

Onions add a sweetness with some complexity to it, a bit of richness, so I would suggest trying a drop of honey, or less processed sugar like Demerara. If you don't have that a sprinkle of a 50:50 white sugar to light brown sugar ought to work as well, just don't overdo it no matter what sweetener you use - if you add too much it will taste all wrong. I'd err on the side of too little than too much.

Another approach may be to add some potato in and let them cook long enough to break down, the starch ought to thicken and will add some sweetness as well. I'd try that on a small scale first to see if it works, you could test it with some beef stock without using any other ingredients.

Turnips.

But use small, young ones, as the large older ones are woody and give off a bit to much of a sulphurous taste. (you want some, to match the onion, but there's enough and there's way too much)

Turnip will mostly dissolve into the broth, making a smooth and creamy but not gelatinous consistency. It should be of minor to mild sweetness, without at all overwhelming the lamb's flavor.

While not the direct substitution requested, this recipe would work well with some Carrot, and some Celery too.

Many cuisines have some backbone to contribute flavor and other things like sweetness. Aliums are a classical part of many of them, but other ingredients usually are added to the alium backbone: Cajun--> bell pepper and celery, French--> carrot and celery, and so on. I'd go with the carrot suggestion but add celery and bell pepper all pretty finely diced and caramelized in the pan first to try and maximise sweetness; you can also look at cooking in some tomato paste in the pan with it (pinçage) The classic French ratio is 1 carrot: 2 onion : 1 celery to try and help with your substitution.

For sweetness, dried fruits: raisins, dates apricots etc. seem cuisine appropriate. Fresh or dried apples might work as well too (I find that they compliment onions, so maybe they'd work as a substitute). Possibly combine these with a vegetable, carrot or turnip, to provide balance. These are in addition to the asefetida.

but onion doesn't only add sweetness due to sugars that it contains, it also makes meat softer, hence it's broad adoption in meat marinades for shish kebabs.

I would try beetroot/vinegar combo. Beetroot for sweetness (also gives natural color), vinegar to make meat soft. Experiment with quantities, but don't go over the edge with vinegar.

I include redcurrant jelly in a lot of dishes to add a bit of sweetness, and now that I've had to cut alliums largely out of my diet (due to IBS not allergies) it's one of my main sources of sweetness in many dishes.

Depending on cuisine though I might also use honey, sugar (white, or darker depending on what I need, or potentially palm sugar or jaggery instead), grated carrot, or finely chopped dried fruit (e.g. sultanas or dates).

I'm surprised nobody mentioned alcohol so far. I have seen the explanation that sugar and alcohol combination softens the meat (actually sugar softens, but alcohol apparently improves sugar penetration into the meat). Unfortunately I've read about it in a different language, but sugar+alcohol seems to be a popular combination for marinating meat. I assume you'd want to marinate it for a couple of hours before cooking, and all the alcohol will disappear during cooking.

P.S.: I assume vinegar might work in a similar way to the alcohol