You can use win32 api.

In one of my apps I do things like that, extend/modify to match your needs. This only use Win32 API and does not lock the file. It's like notepad. When you open a file with notepad it is not locked and can still be written or read by other software.

const
  BUFF_SIZE = $8000;
var
  dwread:LongWord;
  hFile: THandle;
  datafile : array [0..BUFF_SIZE-1] of ansichar;

//create file handler
hFile := createfile(PChar(TFilePanel(FilePanelList.Items[i-1]).LongFileName), GENERIC_READ,
            FILE_SHARE_READ or FILE_SHARE_WRITE, nil, OPEN_EXISTING, FILE_ATTRIBUTE_READONLY, 0);

//set file pointer to beginning of file
SetFilePointer(hFile, 0, nil, FILE_BEGIN);

//read the file
try
    Readfile(hFile, datafile, BUFF_SIZE, dwread, nil);

    while (dwread > 0) do
    begin
      //read/use datafile     
      Here_do_something_with_datafile;

      Readfile(hFile, datafile, BUFF_SIZE, dwread, nil);
    end;
finally
   closehandle(hFile);
end;

var txt : TextFile; 
begin 
  AssignFile(txt,'filetxt.txt'); 
  ReWrite(filetxt); 
  Writeln(filetxt,memo1.Lines.Text); 
  CloseFile(filetxt); 
  Reset(filetxt); 
  while not Eof(filetxt) do 
  begin 
    Readln(filetxt); 
  end; 
  CloseFile(filetxt);

This code works fine for me as a console application, Delphi 2007, running on Win7 64:

Contents of 'E:\TempFiles\Test.txt':

One
Two
Three
Four

Source:

program Project2;

{$APPTYPE CONSOLE}

uses
  SysUtils;

var
  Txt: TextFile;
  s: string;
  AllText: string;

begin
  AllText := '';
  AssignFile(Txt, 'E:\TempFiles\test.txt');
  Reset(Txt);
  while not Eof(Txt) do
  begin
    Readln(Txt, s);
    AllText := AllText + s;

    // Write out each line; comment out to stop.
    Writeln(s);
  end;
  CloseFile(Txt);

  // Write out all content as a single string.
  WriteLn(AllText); 
  ReadLn;
end.

Produces output:

One
Two
Three
Four
OneTwoThreeFour

If you don't want to use the Classes unit, only need to operate on this file, and are making a Windows executable, you could use the Windows unit instead and call the Win32 API functions: CreateFile, ReadFile, CloseHandle and related functions.