Grandfather's suggestions seem reasonable, but maybe you want to do it yourself.
The reason that your system command did not work is that nothing is actually writing to the pipe. You maybe meant:

system "echo $$string | lp -"
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Did you mean $$string? That makes $string a reference; just thought I'd ask.
Since the string could be large it might be better opening a pipe using

open(my $handle,'|-', 'lp -') or die "Oops: $!";
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Then use print to write to the pipe (don't forget to close the handle).