The hash is sorted in a specific order,
That's impossible. Hashes can't be sorted, as you've noticed. Are you sure an AoA isn't more appropriate here? If you wish to continue using a hash, the typical solution it the sort the data as you read it from the hash, as follows:
foreach my $key ( sort { ... } keys %lineFinal) {
...
}
Alternatively, you could use Tie::IxHash instead of a hash. You use it just like a normal hash (thanks to tie), but the contents are ordered.
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