You will need the Terminal for this operation.
Open Terminal and navigate to the directory using the cd command where you want to change the case of the files.
Then run the following command:
for FILE in `ls -A1 *`; do FILENAME=`echo ${FILE} | sed 's/ /\\ /g'`; echo mv ${FILENAME} `echo ${FILENAME} | tr [A-Z] [a-z]`; done
If the output looks good remove the echo string before the mv command.
Please note that this command will fail on file names containing space characters.