Lamp

The Lamp is a reward from the Genie random event and cannot be traded or even banked. Do not ignore the Genie, or you may be transported or have your items scattered, instead of receiving this nice prize.

Rubbing the lamp gives you the option to add experience to a skill, giving xp equal to ten times the current level, not a huge reward, as adding 500 xp to a level 50 skill may not even be the equivalent of a full load of items. 

Using the lamp
This is most valuable in advancing a skill which already has a good level and which is quite tedious to level up. Combat skills are generally a poor use of the lamp, unless you are a 100% pure and value any combat stat xp that does not increase hitpoints.

The best use is normally on the lagging skill of a pair, particularly on smithing if you smith and mine.

Some people like to hold on to the lamp until they gain a level, since it will give 10xp more, but if the loss of an inventory space costs you more than 10xp in training the skill, than that is counterproductive.

Show-offs like to retain the lamp until close to levelling up, so they can have the level-up "fireworks" when they choose.