A bad experience for sure.
But if I was you I would not use the term unfit to fly, as that does imply that you have consumed too much. Instead try something more like taken unepxectandly and suddenly ill.
Then you can use the term that you were denied boarding due to your illness (actually you were taken off the plane, but they certainly didn't fly you to your destination).
Then I would file a claim under EU rules due to denied boarding, and that they didn't take due care of you as an ill passenger and made you walk throughout the whole airport and really push in order to get another flight. I am sure that you will have to go through the Polish regulator, but I think that you would have a case due to your illness.
Also, if the food in the lounge made you ill then maybe you should also consider a complaint with the local authorities in Warsaw for poor hygeine standards? And also mention to LOT when you file your EU claim that their food made you ill.