Rust should only use "closure," lambda isn't used as far as I know.
(I spent a bunch of time trying to sort this terminology when writing the book.)
That said, I don't really know if I'd agree that it's archaic, just less common. Python being an extremely popular language that uses it explicitly (as you say) makes it hard to really suggest that it's archaic.
First paragraph here uses both. I suspect that they use closure throughout the rest of the article, but the fact that they feel the need to reference the other name shows that lambda is still in common currency.
(I spent a bunch of time trying to sort this terminology when writing the book.)
That said, I don't really know if I'd agree that it's archaic, just less common. Python being an extremely popular language that uses it explicitly (as you say) makes it hard to really suggest that it's archaic.