[, ., and / have a special meaning in a regular expression. You have to escape them:
perl -i -pe "s/\[\[\ -f\ \/var\/tmp\/Li\.ksh\ \]\]\ &&\ \/var\/tmp\/Li\.ksh//"
EDIT: beware that this will not delete the line but just remove the text you have in the regex. If if it the whole line a blank line will remain.
More readable version (use brackets to define the regex so that you don't have to escape /):
perl -i -pe "s{\[\[ -f /var/tmp/Li.ksh \]\] && /var/tmp/Li\.ksh}{}"
But, since you are asking about a shell script, why use Perl and not grep -v (--invert-match)?
grep -v '[[ -f /var/tmp/Li.ksh ]] && /var/tmp/Li.ksh' /etc/tl.conf