Do yellow lentils sprout after submersion for a few hours?

First off, no they are almost certainly not dead worms.

What you are looking at inside the lentil seed is the embryo of the future lentil plant. Soaking makes the whole seed expand as it takes up the water, and sometimes the two halves of the seed come apart so you can see these little plant embryos better. But they are contained in the seeds all the time, even before you start soaking them. When you eat peanuts (also legume seeds, just like lentils are), if you look at the inside of a split open one, you can see the embryonic plant really well because they are so big.

Maybe technically speaking, your lentils are sprouting in some microscopic way from the moment they hit the soaking water, but usually when people say "sprouting", they are talking about when the little root of the plant has started to develop and starts poking out of the seed in a visible way. This wouldn't happen in just 3-4 hours. Maybe at the very least a couple days.

As far as the age of your lentils, 30 months isn't too long at all as far as edibility goes (as long as you kept them dry and in decent conditions), so don't throw them out. If you bought them intending them exclusively for sprouts, sorry, I don't know whether 30 months is long enough to diminish their "sproutability" significantly. But I'd be surprised if at least some of them wouldn't start to sprout after a few days.

Also, sorry I can't answer about sprouting more readily depending on the season. Certainly beans will sprout all times of the year, but maybe someone with more experience can say if they do it quicker in the spring or not.

You correctly identified the little white things as sprouts, or technically the plant embryo. (So no insect larvae - phew!)

But assuming that your lentils are already sprouting after three to four hours is a bit optimistic, even in Spring. If you split open a lentil or other legume seed, you will notice that the plant embryo is quite distinctive already when the seed is ripe and dormant. In your case, your lentils are actually peeled and halved¹, which will of course expose the embryo, which is usually hidden between the two halves of the seed. So I’d expect less than 50% of your lentils to have the white thing - less, because it’s a bit brittle and some will have fallen off during production, handling and storage. You should be able to see them in the dry lentils and even better now that they are soaked: they get lighter after a while.

Lentils are pretty robust if stored reasonably, so unless you noticed a rancid smell, your batch should be ok to cook. (Split lentils are sometimes oiled very lightly, and this oil can get rancid, hence the smell check.) You might have to cook them a bit longer, but that’s about the only issue with older lentils I would expect.

Side note:
If you want lentil sprouts for the kitchen, make sure you use whole lentils and soak them for a few hours, then rinse and drain twice a day. The usual time from seed to sprouts is four to six days. And in this case, “fresh” ( < 1 year) seeds are the safer bet.

¹ In Indian cuisine, split lentils are a staple for dal, in western cuisine, split peas are used similarly. Hulling decreases cooking time and gives a smoother end product.