Arenas in Rust work very well with lifetimes. In fact arenas benefit greatly from lifetimes, because lifetimes allow them to uphold the usual Rust safety guarantees about preventing use-after-free. For example, here's the bumpalo crate in action:
let mut arena = Bump::new(); // create arena
let foo = arena.alloc(Foo { x: 42 }); // allocate item in arena
bump.reset(); // clear arena
foo.x += 1; // compiler error preventing use-after-free