This should work too:

use Algorithm::Diff qw( LCS_length );

sub in_list {
    # Returns true if lsa is a proper subsequence of lsb
    my ($lsa, $lsb) = @_;
    return LCS_length($lsa, $lsb) == @$lsa;
}
[download]

And a module-less solution:

sub in_list {
    # Returns true if lsa is a proper subsequence of lsb
    my ($lsa, $lsb) = @_;
    my $ia = 0;
    my $ib = 0;
    for (;;) {
        return 1 if $ia == @$lsa;
        return 0 if $ib == @$lsb;
        ++( $lsa->[$ia] eq $lsb->[$ib] ? $ia : $ib );
    }
}
[download]

Update: Added second solution.
Update: Sorry, I missed the bit about this being homework.