Deleting a hash element returns its value, so if you define the %availableNumbers hash like this:

my ($lidno, $perbin, %lists) = (10, 10);
my %availableNumbers = map { $_ => $_ } 1..$lidno*$perbin;
[download]

you get to choose and delete at the same time.

for my $lid (1..$lidno) {
    my %deck = %availableNumbers;
    $lists{$lidno} = 
        [ map { delete %deck{ (keys %deck)[rand( keys %deck)]}
               } 1..$perbin ];
}
[download]

That could have been folded into another map, but enough is enough ;-)

After Compline,
Zaxo