You can read in the text to an input buffer (tstringlist or memo)
and append the wanted lines to an output buffer:

//Pseudocode:
4counter = 0;
marker = 0
Repeat
  begin
  line := buffer[marker];
    if line  <> ''
    then
      begin
        //Copy 1, 2 or 3 empty lines to outputbuffer, but not 4
         if 4counter > 0 buffer.add('');
         if 4counter > 1 buffer.add('');
         if 4counter > 2 buffer.add('');         
         buffer.add(line);
         4counter = 0;//reset to zero empty lines
      end
    else
       inc(4counter);
 
    if counter = 4
     then
       begin                 //drop the current 4 empty rows
         4counter = 0;  //start counting the next 4 rows 
       end;

    inc(marker);
   until
     marker > buffer.count;
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