I think the OP is specifically trying to say that most lay people do not actually mean "life expectancy at birth" when they use the term "life expectancy", but

I think the OP is specifically trying to say that most lay people do not actually mean "life expectancy at birth" when they use the term "life expectancy", but instead mean "how long I, a person who has reached adulthood, can expect to live". I agree with OP, FWIW.