I don't think taht the faking part of empathy that is typically expressed here is really lying, it's more of a trying to be normal and like others. No one sets out to "act nice" to deceive another person or lie.

In addition there is not a soul on this earth that does not do this to some extent. Everyone fakes "nice" and caring at times. Sometimes we have to to get by in certain situations. Like an office party, you might really loathe your boss but do you show that in the office party or even in the office? no. Is this lying? Is it deceitful? no it's part of the social norms.