Conocer and Direct Objects

Question

· I know him: Le conozco / Lo conozco· I know her: Le conozco / La conozcoThere is a lot of discussion on the internet about whether “him” and “her” are direct objects of conocer that should use lo and la.

Answer

Hola Joseph
Yes, it is a non-stop topic! 
The cases you are mentioning there are correct except for "le conozco" referring to "her". That use of le instead of la as a direct object pronoun is not accepted by RAE.
Saludos
Inma

Answer

According to my Grammar book (by Butt & Benjamin), the "Academia" in Madrid tried to decree that "lo" should always be used for direct objects referring to male human beings, but they relaxed that directive in the face of massive resistance in peninsular Spain, particularly in the northern and central regions; (the use of "lo" is, however, standard practice in Hispano-America).