A couple minor points. First, "! -z" is more commonly known as "-n". Second, if you're running perl from the commandline anyway, use lib is usually called -I, while all other uses are called -M. And rather than dealing with lots of annoying quotes, just pass in your parameters.

figlet()
{
    local que=$1
    local fu=timesofl

    if [ -n "$2" ]
    then
        local fu=$2
    fi;

    if [ -n "$que" ]
    then
        perl -I$HOME/path/to/installed/FIGlet.pm -MText::FIGlet -e 'pr
+int Text::FIGlet->new(-f=>$ARGV[0])->figify(-A=>$ARGV[1])' "$fu" "$qu
+e"
    fi;
}
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Unlike in perl where quoting a variable is a waste of time, in shell it's imperative to keep any embedded spaces unchanged. Having moved your variables from inside the perl code to purely in shell, I need to keep the quotes - but I can get rid of leaning toothpick syndrome (LTS). And then I can switch your double quotes to single quotes and now I think the whole command is much easier to look at. Personally, I would have made the whole thing just a perl script to begin with:

#!/usr/bin/perl
use lib "...";  # probably not really needed.
use Text::FIGlet;

my $figlet = Text::FIGlet->new(-f => $ARGV[1] || 'timesofl');
print $figlet->figify(-A => shift);
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Of course, I'd add more comments and whatever. ;-)