Why did Heiji's mom have to lie to Mouri and Conan in episode 220?
Her first three lie about her cooking skill, allergies, and the fact that she is married was intended from her to test Mouri whether he noticed it or not, not to hide her real identity as Heiji's mother. But her third lie came unintentionally from her when she was about to say cold coffee. Maybe she did it accidentally and has to cover it with saying "Reiko".

So she lied to test Mouri, not to hide her real identity.

Another possibility is maybe she didn't know whether Heiji told his friend about her hobby and others or not, and she did that because she didn't want to know that she is Heiji's mother and make all her lies vain.