Not sure if this is the right spot for this query, but here goes.
My MC is a mentally ill teenager who was feeling trapped by one of his friends, and so he used something - a common bedroom item, I'm hoping, maybe a lamp - just to hit him with, but he ended up dying.
What would be the best object to use for this?
It can be one of many, sure, depending on how strong the MI teenager is, the weight and material of the lamp, and the number of times he strikes the victim. I don't know what your victim looks like, his or her mental acuity, etc, but to me it seems that the MI teenager would have to repeatedly strike the victim on the head, or deliver one heavy blow with something stronger and solid, like a large book (saw bible mentioned). Whose bedroom is it? A man's or a woman's? Is it a familiar or strange place for your MC -- that might also determine what he chooses to use if he feels threatened.
A baseball bat or solid object (as mentioned) is better. DCVermillion also made a great point... falling is a great method for an accidental death. No weapon so it removes the concern about logistics and you can have the victim land on something to ensure a swift death. The neck could break, or depending on where they land its enough blunt force trauma to cause bleeding in the brain. Also, it would make more sense given the mental state of the teenager to use shoving or pushing; however MI can mean many things... I'd love to know what's his condition, since that might also help you determine what your MC would do in a situation where he feels trapped.