这样：
function TForm1.MemoLinesShowing(memo: TMemo): integer;
var
  R: TRect;
begin
  Memo.Perform(EM_GETRECT, 0, Longint(@R));
  Result := (R.Bottom - R.Top) div Canvas.TextHeight('XXX');
end;

问题是，TForm 和TMemo 需要用同样的字体。
如果不同，可以用以下代码：
function TForm1.MemoLinesShowingLong(Memo: TMemo): integer;
Var
  Oldfont: HFont;  {the old font}
  DC: THandle;     {Device context handle}
  i: integer;      {loop variable}
  Tm: TTextMetric; {text metric structure}

  TheRect: TRect;
begin
  DC := GetDC(Memo.Handle); {Get the memo's device context}
  try
   {Select the memo's font}
    OldFont := SelectObject(DC, Memo.Font.Handle);
    try
      GetTextMetrics(DC, Tm); {Get the text metric info}
      Memo.Perform(EM_GETRECT, 0, longint(@TheRect));
      Result := (TheRect.Bottom - TheRect.Top) div
         (Tm.tmHeight + Tm.tmExternalLeading);
    finally
      SelectObject(DC, Oldfont); {Select the old font}
    end;
  finally
    ReleaseDC(Memo.Handle, DC); {Release the device context}

  end;
end;