That is a high voltage drop....
ARe you SURE your LCD is a low current LCD??? There are LCD's out there that take 300 mils to run! I happen to have 2 of them...And they will blow a unsinked 7805 in a extremely short time... and will blow a 7805L in a even quicker time.

How about your LCD's display contrast? is it adjusted correctly? usually a 10K pot with center going to your contrast pin and ends going to +- is all that is needed....Adjust pot until black squares show up. Some LCD's do not need this pot...Some do.

Dwayne