Is it necessary to apply lotion to your hands after washing each time?
If you are talking about applying antibacterial lotion after following proper handwashing procedures then I would say no. The skin has natural oils that help to keep the skin moisturized.
The CDC has a procedure that should be followed when washing your hands. They recommend applying soap to the hands and working up a lather, using warm water if possible. Hands should be scrubbed for at least 15-20 seconds. Dry hands with a paper towel or hand dryer. Also, use the towel to turn off the faucet to prevent the spread of germs.
If you are talking about applying lotion in general then it depends on whether your skin is dry or not. I find that I need to apply more lotion in the colder months. Otherwise my hands tend to get very dry.
Putting on lotion after washing hands is not stipulated in the universal precautions. The important thing is the washing. Lotion is highly encouraged however, if you are washing your hands several times a day, to prevent chapped dry skin and torn cuticles. When I worked in a kitchen at a summer camp we had "moisturizing hand soap" for those of us washing our hands multiple times a day. It eased the dryness, but didn't prevent it. I found that a quick absorbing lotion was better than something greasy though - because if your hands are full of oily lotion it just gets everywhere.