Lemon tree [Update]
I have taken aware of the mealybugs infestation (thanks to BushDoctor) and I have been spraying neem oil on it. Should I do it thoroughly, like everywhere? I heard the plant can absorb neem oil and use it for themself, is that true? Anything else I should do to help it atm?
Yes, make sure you treat the tree, leaves and also the undersides of the leaves.
Also remove the fallen leaves from the soil and dispose of.