The tree has been outside during the summer, since a few weeks back I took it in. A few days back I noticed these strange things attached on the back of 20% of the leafs. What is it?
This appears to be mealybugs on your lemon tree. If you can isolate a few and examine under magnification compare to the images here and see if they match up. If the plant is reasonably small one simple treatment is to use a Qtip and rubbing alcohol to wipe off the patches you see. Keep a watchful eye for new patches, and repeat until they are all gone.
While manually removing the white goo (whatever it was) with a few cotton pads, I noticed a few white flies. After some googling, I found a matching picture of a whitefly. The liquid drops seems to be Honeydew, which is "a sticky byproduct of their feeding, may coat leaves and anything under the tree, such as benches or vehicles." (see this article for more info)