I just used the lasso tool to place an object from one picture to another. How do I remove the bits of the old background from that obeject?
You need to select the bits of background with the lasso tool and delete them.
You can also carefully try using the magic wand or the brush selection tool (click and hold the magic wand to reveal) The brush selection tool works pretty well if you want to make a selection without too much effort. Of course all of these methods are the simpleton way to do it.
I would try creating and dragging anchor points with the pen tool and making a selection from that. It is much more accurate at making selections.
You can also try going to Select