There is no manga that I know of that would be more canon than the anime. So do not worry about "not having read the manga".
The advantage of having Gilford mistake Lelouch for Cornelia is that he can leverage Gilford's loyalty to continue giving him orders as long as the Geass is under effect, and having Gilford take whatever initiative necessary that is advantageous to him.
For example, after Gilford had vanquished the guards, he was able to have Gilford take him to a location of his choosing. A simple order to "protect him" would probably have made him a standing duck, as the Geass would have lapsed or stopped driving Gilford to action, as soon as Lelouch was "safe".
That ties in with my opinion that the practical reason for Lelouch not to give blanket orders for people to obey him (as he began doing after some point) was that doing so basically reduces people into living robots without initiative or self-preservation.