Now I installed lzRichEdit and can confirm your issue with the missing pages. A quick test shows, however, shows that the problem seems to disappear if the RichEdit is created at runtime:
procedure TForm1.FormCreate(Sender: TObject);
begin
lzRichEdit := TlzRichEdit.Create(self);
lzRichEdit.Parent := TabSheet2; // 2nd page of the page control as in your example
lzRichEdit.Align := alClient;
// etc. - set other properties
end;