I do not see any signs of insects. The spider is harmless. In fact it may eat the harmful insects. Do not use organic fertilizer. Use Foliage Pro 9-3-6 instead according to manufacturer's directions. Remove the small fruits from the tree with only a few leaves so that it can use the energy to recover instead of making fruit grow. The yellow is not sun burn, it is probably nutrient deficiency possibly due to use of organic fertilizer.

Could it happen over a day or two? I believe that one morning leaves were fine and in the evening I found circular lines on them, like after some pest.

Google citrus leafminer

Thank you both response. Today I met some invaders but I'm not sure if it's leafminer and it could be a cause of my all troubles. It creates cotton/spider web like nest. I found them all in flowers and leaves next to them have this weird marks. So far I removed all bloomings but lemon has only 4 leaves left.

I don't see any damage that might have been caused by a caterpillar.