Is it unethical for a professor to lie to their students?

Yes.

Is is still unethical if the professor argues that the lies were for the students' own good?

Yes.

Is it still unethical if, a few months into the course, the professor tells the truth?

Yes.

Is it still unethical if, a few months later, the professor tells the truth and one or more students says "you know, I understand now why you lied to us"?

Yes.

This really isn't a challenging conundrum. The student-teacher relationship is a special one. There are expectations that need to be fulfilled on both sides. One of the most basic ones that can be expected of a teacher is don't lie to your fucking students.

This doesn't answer the prompt at all, which is: how do you define 'ethics'?

It could be considered a non-lie under the concept of mental reservation. In older usage, coding a computer meant writing assembly or machine language only; thus, a report on FORTRAN indicates that "FORTRAN virtually eliminates coding and debugging". This is a standard usage of the word coding although slightly archaic.

http://www.softwarepreservation.org/projects/FORTRAN/BackusE...

Otherwise, presenting informal proofs to students in engineering or science that would not be considered mathematically rigorous would also be a lie and unethical.

Possible overreaction alert...

Lying always being unethical is actually a relatively standard idea in classical ethical theories e.g. Summa Theologica, Question 110, Article 3. However, the statement that the class involves "no coding" could be considered truthful in the social context or as part of a use of mental reservation.

Lying can be perfectly okay under consequentialism, which also goes way back. Personally I'm not very convinced of ethical theories where lying is unethical in all circumstances (sorry Kant), and I suspect I'm not the only one. Stating that there exists an ethical theory that supports your point just isn't very convincing for people who don't subscribe to that particular theory.

Who is the professor to judge what is for someone's own good or not?

That is literally the job of a traditional educator.

Their job is to educate, and stimulate the mind. They aren't telepathic, any "for your own good" they engage in is born of assumptions unless they know the student well.