Broke my Lumia 820 LCD. Can I just swap it with another Lumia 820?

So, yeah. Dropped my phone and the LCD is cracked. The digitizer seems to be fine. So I was wondering if I'll run into any issues just buying another (used) Lumia 820 and using it for parts, such as the LCD.

PS: I need to know, because Windows Phone 8.1 is about to come out and I ain't havin' this back-up laggy Android shit. (Joking, but not joking)