Your debug output from the two scenarios seems to indicate that the WiShield is able to connect to twitter.com and tries to send a tweet in both the cases but when you have the lcd enabled, twitter does not like what it received and therefore returns with a failure.
One possible reason might be that you have a lot of local variables declared and there is not sufficient RAM space available on the MCU. Try removing some of the unused variables and also the Serial library. You can use avr-size to verify if you have sufficient SRAM.
Also, which device are you using on your Arduino? 168/328?