Keep the previous line in a variable or at least keep its length or position (via tell()) in a variable to seek() back if you need:

my $p;
while(<FILE>){
   #du stuff
   if( prevous line needed and defined $p ){
      seek FILE, -(length()+$p), 1;
      my $prevous_line = <FILE>;
      # next <FILE> will return the current line again,
      # so call it again before going on!
  }
} continue { $p = length() }
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