But the tree has been out of the pot three times since February

Evaldas, it is your tree and you certainly can do with it whatever you wish. When you had the tree out of the container did you check to see if the main root ball was dry, and also check for root damage or medium compaction? The tree's problem must be one of the three issues listed above. If everything was OK, the tree would not be having this difficulty. I'm afraid if you do nothing to correct the situation, the tree is going to die. I seriously doubt that your tree's problem comes from a citrus disease, as there are no citrus diseases located in Lithuania. It looks to me that because of one of the above issues, the tree's foliage desperately needs water. The best to you and your tree. - Millet (971-)

Millet, would it be OK to repot this Calamodnin into a smaller clay pot, with only one drainage hole?

Most any container with drainage would be OK, but the concerns about the root system's health, the root's aeration, and the root's compaction still remain a concern. If the irrigation water was simply running down the sides of the tree's root ball, due to being in an over sized container, then a container having the proper fit for the size of the tree will certainly help to increase the amount of water actually passing through the root ball. But if the root ball does not have good aeration, thus poor drainage, the problem will not be corrected. The best - Millet (970-)

I tried to water it more thoroughly and here's what happened

The branches started to turn brown, I guess the roots are short on oxygen... I'll get to repotting it on Monday...
Oh, and since all the leaves on the tree had obvious signs of being dry and it was apparent that they wouldn't come back to normal, I took them all off, so now the tree is completely bald.

IMHO, this is a root rot and it is to late to save the plant.
Sorry.

Sylvain, well I really hope you're wrong , but anyways we'll find out on Monday.

Millet, I know I asked so much, but I still have a couple of questions. As I'm going to repot it on Monday, I bought some pine bark. Do I need to prepare it with hot water? Because I read in an orchid care book, about preparing the medium, it said, quote on quote "Whatever potting material or mix you choose — whether you mix
it yourself or buy it ready-made — it must be wetted before you use it. Otherwise, it will never hold moisture properly and will always dry out. Here’s how you do it: <...> Fill the bucket with hot water. Hot water penetrates the material better than cold water". Does the same apply for citrus?
Also, I'm going to post a picture of the roots, hopefully you'll tell me if they're rotten or not, and if I still can expect something from this plant.

Yes,it is wise to pre-soak the bark, before you use it. Soak it over night. -Millet (968-)

I've decided to repot the tree today.
So as I was just about to plant it into pine bark/peat moss medium and because I'm not expecting much from this tree I've decided to plant it into simplest black peat/soil medium (the similar stuff it was in when I purchased it), we'll see where this leads, it's going to be an experiment.
Here are the pictures of the terrible roots, but no rot luckily:

> Here are the pictures of the terrible roots, but no rot luckily
It IS root rot:
- there is nearly no more small roots (hairy root). Rotten away.
- the medium sized roots are brown not whitish.
- the "big" roots' ends are black.

The only (tiny) chance to save that plant would be to soak the roots in an Aliete solution for one night. Then to repot it in a very aerated substrate.
And to keep it out of sun and dryness. Going on the Aliete treatment.

But the tree has been with this amount of roots in such condition for 2 months, and the branches are still green. I think they would've turned brown a long time ago, if they were in such horrific condition.

Evaldas,
You are pushing your tree too much.
Listen to others.
What ever you do, keep that tree shaded.

Voila