I've been trying to do this in perl6, I can get your solution to work - perl6 may well have changed in the meantime.

In fact I get an error message about the =$

...
Preceding context expects a term, but found infix = instead.
Did you make a mistake in Pod syntax?
...
------> for =^$fh -> $line1, $line2 {
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I had thought that something like this might work:

my $fh = open("file");
for $fh.lines,$fh.lines -> $line1,$line2 {
    say $line1;
    say $line2;
}
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but this seems to produce a rather confusing result with all the lines stuck together is a Seq, and has some EOF related error, the 'singluar form':

for $fh.lines -> $line {
    say $line;
}
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works fine.