He didn't realize that Peter hadn't already fired him. Alicia was sworn to secrecy because she was involved in the process, but Eli would not have known anything about it had he not seen Cary as he was walking around Lockhart Gardner. So he wasn't told it was secret.

It was mentioned that she had a brother but not that he was gay

No, he did pay her that was the point. It was him that paid her. He wouldn't have paid her if he had known she was already being paid for by someone else. That was his defense. Someone was paying the prostitute as an attempt to bribe him, but he didn't know that because he was paying her as well so he was not corrupt.…