TMSFNCListEditor not showing image immediately after assigning image

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;