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24V,,........ Are you crazy??? do you know the maximum input voltage of 7805.... Not more than 18V to 20 is max it can withstand... definetely the power dissipation is more so the regulator gets heated up and would get burnt if you operate at that voltage....
The heat is the product of voltage being dropped and the current flowing through it. Most if not all 7805 will withstand 30V quite happily but only if the current is low enough that the heat generated is tolerable.
An LCD should draw virtually nothing in terms of current, the only thing that might present a heavy load is an LCD backlight. If a backlight is in use, try feeding it through a suitable resistor from BEFORE the 7805 instead of after it.
As said, 7805 operation is specified for 25 or 30V Vin in the datasheet, of course only usable at suitable low loads. In addition, it won't "burn" if thermally overloaded, but go to thermal shutdown. Operating the device at these temperatures will surely affect it's lifetime, however.
If the high current consumption is normal operation, you won't get happy with your design unless using a switching regulator, I fear.