When it comes to Elvis Presley lamps, there are three major types. First is your standard-looking lamp but with an Elvis figure on the bottom area. The second variety is a picture of Elvis imprinted on the lampshade. Lastly, there's an Elvis figure, and the light is coming within.
Since the first two are similar to buying a standard lamp, you need to consider if you want ambient or task lighting if you choose to buy any of these types. As a quick generalization, ambient lighting comes with the purpose of providing general illumination. On the other hand, task lighting is used in giving light to help you do some paperwork, draw, read and any other desk task.
The third type is generally for aesthetic purposes. Hence, if you want this type, your primary concern should be how the lamp's style fits into the overall theme of the desk and/or room.