I believe it's possible to do this, but it's probably not going to be easy. Were it simply a PC monitor, it would be far less hassle.
Essentially, the laptop you've bought is going to have to have either of two things. A VGA input socket somewhere, so that you could use the laptop as a monitor for another system. If it has one of these then you'll need to look on the net for "VGA adaptor" that's compatible with PAL Xbox consoles. You connect the standard Xbox TV leads to this adaptor and the adaptor fits into VGA ports (which CRT monitors use, an additional adaptor might be required for LCD monitors).
Or, your laptop needs a video card with a video-input port, usually in the form of S-Video. This isn't a standard feature on laptop GPUs, usually it's only included on higher-end versions of laptop graphics cards. If it has one, you should be able to connect the Xbox to it there, providing you have an Xbox S-Video lead, which again wouldn't come with the console as standard and would have to be purchased separately.
Unfortunately, even after all this, the picture on the LCD screen of the laptop wouldn't be all that great. Computer displays are very high resolution compared to standard-definition home TV sets. Which means that when you put low resolution video onto them that was designed for TVs (which is what the Xbox outputs), the image is likely to lack definition and/or suffer from very pronounced aliasing (which is the graphical phenomenon that causes all outer vertices of computer graphics to look pixelated and suffer from a "stairstepping" effect).