My attempt (not keen on the redo loop):

#! perl -slw
use strict;
use threads stack_size => 4096;
use threads::Q;
use Scalar::Util qw[ dualvar ];
use constant { TRUE => dualvar( 1, 'true' ), FALSE => dualvar( 0, 'fal
+se' ) };
use enum qw[ LEFT RIGHT ];

sub fringe {
    my $tree = shift;
    my $Q = threads::Q->new( 1 );
    my $scan; $scan = sub{
        my $t = shift;
        !ref( $t ) ? $Q->nq( $t ) : ( &$scan( $t->[LEFT] ), &$scan( $t
+->[RIGHT] ) );
    };
    async{ $scan->( $tree ); $Q->nq( undef ); }->detach;
    return sub{ $Q->dq; };
}

sub sameFringe {
    my $i1 = fringe( shift );
    my $i2 = fringe( shift );
    {
        no warnings 'uninitialized';
        ( my $v1 = &$i1 ) == ( my $v2 = &$i2 ) or return FALSE;
        redo if defined( $v1 // $v2 );
    }
    return TRUE;
}

my $a = [ 1, [ 2, [ 3, [ 4, 5 ] ] ] ];
my $b = [ 1, [ [ 2, 3 ], [ 4, 5 ] ] ];
my $c = [ [ [ [ 1, 2 ], 3 ], 4 ], 5 ];

print sameFringe( $a, $a );
print sameFringe( $a, $b );
print sameFringe( $a, $c );

my $x = [ 1, [ 2, [ 3, [ 4, [ 5, 6 ] ] ] ] ];
my $y = [ 0, [ [ 2, 3 ], [ 4, 5 ] ] ];
my $z = [ 1, [ 2, [ [ 4, 3 ], 5 ] ] ];

print sameFringe( $a, $x );
print sameFringe( $a, $y );
print sameFringe( $a, $z );

__END__
C:\test>lazyTree.pl
true
true
true
false
false
false
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