No, there is no way the lamp can have that effect. It's just an unfortunate coincidence that the problem cropped up after the lamp change.
The problem is with the projector itself, either the driver circuit, the display chip or the connections between the assemblies. You should be able to see if it's the connections by using a non-conductive probe ( a wood stick ), to gently put pressure on the boards while the projector is running to see if that has any effect. That means the projector has to be running with the top off.