Sure, you can find lecture theater and lecture theatre in American usage—but not easily. A COCA search returns 7 results for the former and 4 from the latter. One is from an interview with a Canadian on a National Public Radio broadcast. One is from an article by a British author. One is from a magazine article about an exhibit in London. Four are from academic publications, and four from fiction. There are zero results in COHA and in SCOTUS opinions, and only two in the Time magazine corpus, once each in 1944 and 1973.
I would label lecture theater and lecture theatre as obscure in American usage. Not that I am any kind of typical, but this term is obscure to the point where I, an American who is active in university alumni affairs and who attends many events at universities, but is not an academic, would need to think about what a lecture theater could be if told to go to one.
Lecture hall is the term I use; it has two orders of magnitude greater results, with 321. If you look at the Google NGram, lecture hall has a much higher relative prevalence over lecture theatre in the American corpus than in the British.
Furthermore, I only associate lecture hall with such a facility at an academic institution. A term encompassing both academic and non-academic facilities would be auditorium, which is vastly more prevalent in both corpora. COCA has 3300 results, so another order of magnitude above lecture hall.