I have not see this done but a good thought...the first step would be to remove the old EL display so you can backlight the LCD panel from behind. If you are going to this much effort, there are several sources on the internet where a replacement backlight can be purchased, just replace it. The original EL display runs at 60VAC off the secondary of the step up driver transformer...Do not connect any LED's to the old EL connection...If you can find a Service manual, there are many easy to get to 5V/8V/12V B+ points to connect to...Most folks want the display to be on 100% of the time so tie them to a power supply.
Let us know how you make out with this project...a photo would be nice to see.
Enjoy
Wmbio