The elements of @lines has newlines. You either need to chomp them:

chomp(my @lines = <FILE>)

In which case you print them with:

print FILE for @lines;

# or, to be more verbose

foreach my $line (@lines) {
    print FILE $line
}
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Or, you can leave off the chomp, and use the loop:

print FILE "$_\n" for @lines;

# or, to be more verbose

foreach my $line (@lines) {
    print FILE "$line\n";
}
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Either you've removed the newlines or you haven't, your foreach loop has to match.

Of course, if this is all you're doing with @lines it'd be much simpler, and more kind to memory, to just read and write at the same time:

print OUTPUT_FILE while <INPUT_FILE>;

# or, to be more verbose

while ($line = <INPUT_FILE>) {
    # manipulation of $line goes here.
    print OUTPUT_FILE $line;
}
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perldoc -q 'entire file' covers this topic, 5.6.1's perldoc -q 'line in a file' helps to explain dealing with files, and 5.8.4's perldoc -q 'line in a file' tells you to use Tie::File.