The answer would be a qualified NO.
The wiring connections to the screen would have to match between the old display and the new. By that I mean that the wires coming from the system board would have to perform the same functions when connected to the same points on the new display. For this you would have to know the internal wiring details of both the old and the new display panels. It would also have to have the same type of cable connector as well.
One way that might possibly work is to open the phone and see if there is a part number printed on the back of the LCD panel itself. Using just the number try searching online to see if you get results.
Don't be surprised if the results are from a manufacturer whose name bears no resemblance to the name on the phone.
Most LCD panels be it for TV, Monitors , Phones etc., are made by specialist LCD panel manufacturers who make to order for the device manufacturer. Also don't be surprised that even if you find the manufacturer that you will not be able to purchase it directly from them.
You could also search places like Ebay etc where your particular model phone may be offered for sale as faulty good for parts where it appears that the LCD screen is undamaged and possibly still working but cannot verify as the phone doesn't work at all. You could always contact the seller and ask was it working before the phone failed, was the phone dropped etc., and hope for honest answers. Then it depends on how much you are prepared to gamble, money wise, hoping that the LCD is at least OK, so that you can swap it over.
If you have two identical phones, one with a faulty screen and the other with a working screen but not working otherwise then you could swap the good into the faulty but to re-purpose it between different brands or even different models you would have to know its' input wiring connections so that it would be suitable to use somewhere else.
As you can see from the schematic (scroll down a bit) in the link below the example shows the LCD having 16 input leads. There is no standard as to what function goes onto what input as the LCD manufacturer would make to order from the device manufacturer to suit whatever particular requirements.
The best that I can suggest is that you offer it for sale (or for free) as faulty -good for parts, LCD works on places such as Ebay, Gumtree, etc. to minimize the amount going to landfill. You might be surprised at the response as usually the major problem with devices is a broken screen which is hard to source, especially on the lesser known brands. So if it is re -usable by someone else you have minimized, as best you can, the amount going to landfill (the other phone is repaired instead of replaced, again with less landfill and your phone has less parts being sent to landfill by the new owner - basically one completely faulty phone being sent instead of two partially faulty), and also perhaps you have recouped a little cash towards the purchase of a new phone.