There should be no issues with the LCD screen.
Since you found a place in Italy to upgrade the notebook, I assume they can order the parts for you and tell you if those cards are compatible with your notebook. Mobile graphic cards follow the MXM format and ranges from Type I to Type III. Type III cards are largest and therefore would be the format the Mobility Radeon HD 5870s would use.
The real concern is if it is actually be worth it for you to upgrade right now. XFired HD 5870s is still a very high end solution, therefore upgrading them to something faster my not give you enough of a performance increase to justify the amount of money you will be paying.
Trust me, you will be paying for that upgrade. Generally speaking a laptop video can cost 2x more than their desktop counterparts; probably more for high end cards. Let's just pretend that two HD 6970M will give you a real performance boost over your HD 5850s, the price of each HD 6970M may be $600. Therefore, the price of the upgrade will be $1,200 just for parts. Don't forget taxes and labor. If you install the cards yourself, then you can save on labor.
In this pretend situation you have to determine if XFired HD 6970M performance is really worth the amount of money you'll be dishing out. Unless of course you have money falling out of your ass. Man, I wish I had that disease.