Hello fellow countryman
I just came across this thread, so I hope it's still relevant despite its age...
I don't think you can buy LED backlights for LCD displays because (in my experience at least) if you remove the LCD display itself from its PCB (so you can access the backlight and replace it if you have a new one), when you put the display back you'll never be able to get the contacts to touch properly. I think they use some sort of vacuum method in the factories to assemble them.
These days, LCD displays are so cheap it's not even worth messing around with this (I've asked about the same thing as you before coming to this conclusion). I've bought several displays (with LCD backlights) from
Eastrising/BuyDisplay.com in China (they also have an
eBay store). Seems like high quality displays in a variety of different sizes and differently coloured LED backlights. Oh, they also have downloadable datasheets with pinouts etc which is useful when replacing an existing one.