Since it's easy to do this with an array — simply look at element at index $i-1 — you could load the file into an array, process the array, then write the array back out to the file. Of course, this doesn't scale with the size of the file well. For a generally application solution, you could map the lines of the file into an array using the module Tie::File:

use Tie::File;

tie my @array, 'Tie::File', "file.txt"
    or die "$!";

for ( my $i = 1; $i <= $#array; $i++ )
{
    if ( check( $array[$i] ) ) # the "current line"
    {
        modify( $array[$i-1] );
    }
}
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In this example, I started at index 1 (the second line) because even if the first line (index 0) passes the check, there is no "previous line" to modify.