Did you see the information on Naviance/similar or on the school admissions website? For Washington and Lee at least, it says they are not required and I got in RD without them. I did email admissions to confirm while I was still considering whether or not to apply and they said they would be considered if submitted, but a student would not be penalized for not having them. I was not a finalist for the Johnson scholarship, however, and that seems to be a consideration for you as that’s the only merit they have available.
I’m afraid I don’t know as much about Davidson, but a quick perusal of the website told me that they officially say the same thing about subject tests as W&L. I checked both schools’ Common Data Sets as well. W&L’s says “Considered if submitted” and Davidson doesn’t say anything at all.
I wouldn’t go so far as to say that they’re truly optional, considering I come from a rural public high school in a state that’s underrepresented at W&L. If you’re at a school/living in an area where it’s common to take them, I suspect it would be a good idea to take them too. However, if your student doesn’t do well, I suspect it won’t hurt them as badly to not submit as it would at a place that recommends SAT subject tests.