There are a lot of special regex characters in your string which need to be escaped to be properly matched.

Something like this is probably what you are looking for

foreach(@lines) {
    if (s/^\#\<\-\(0N\<\-\(s3T$/*<-(0N<-(s3T/g) {
        push @newlines, $_;
    }
}
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Adding the ^ (beginning of the line anchor) and $ (end of the line anchor) is important so you don't get any partial matches