Stuff file2 contents into a Perl data structure, such as a hash of hashes, then print desired file1 contents using array slices:

use strict;
use warnings;

my $fh;
open $fh, '<', 'file2.txt' or die "cant open file2.txt: $!";
my %info;
while (<$fh>) {
    if (/^>(.*)_left\s\w+=(\d+)/) {
        $info{$1}{left} = $2;
    }
    if (/^>(.*)_right\s\w+=(\d+)/) {
        $info{$1}{right} = $2;
    }
}
close $fh;

# comparing with file 1
open $fh, '<', 'file1.txt' or die "cant open file1.txt: $!";
my $id;
while (<$fh>) {
    if (/^>(\w+)/) {
        $id = $1;
    }
    else {
        my @nums = split;
        my $len  = $info{$id}{left};
        print ">${id}_left length=$len\n";
        print "@nums[0..($len-1)]\n"; 
        $len = $info{$id}{right};
        print ">${id}_right length=$len\n";
        print "@nums[($#nums-$len)..$#nums]\n"; 
    }

}

__END__
>AAAT3R_left length=6
40 40 40 40 40 40
>AAAT3R_right length=62
40 40 40 40 40 40 38 38 37 39 36 36 40 36 35 35 35 38 40 35 35 33 35 3
+5 35 40 40 40 40 37 37 38 38 38 40 40 40 40 40 40 40 40 40 40 40 40 4
+0 40 40 40 37 36 36 31 22 22 22 20 20 20 20 20 14
>AAA2OJ_left length=14
18 18 18 21 35 35 35 32 32 32 33 35 38 39
>AAA2OJ_right length=14
37 37 37 37 37 37 33 32 32 30 20 17 17 17 0
[download]