This is because the image is cached and being asynchronously loaded. You can try the following approach
procedure TForm1.DoImageCacheReady(Sender: TObject);
begin
TMSFNCListEditor1.Invalidate;
end;
procedure TForm1.WebFormCreate(Sender: TObject);
begin
TMSFNCListEditor1.Items[0].LeftImageName := 'Item1';
end;
procedure TForm1.WebFormShow(Sender: TObject);
begin
Application.OnImageCacheReady := DoImageCacheReady;
end;