The technique of displaying data on LED is quite different from LCD. Todays LCDs comes with inbuilt driver chip to which we just have to supply data and rest of the work is done by it. Where as in case of LEDs we have to use the refresh technique.
If your LCD structure is same as that of LED board having 7x40 Dots then its very easy to port from LED to LCD. Just make the same connections as that on LED board with 10k resistor (not actually required) in series with the 7 data bus lines.