As long as the type is generic on the allocator, the lifetimes of the allocator don't appear in the type. So eg if your allocator is using a stack array in main then your allocator happens to be backed by `&'a [MaybeUninit<u8>]`, but things like Vec<T, A> instantiated with A = YourAllocator<'a> don't need to be concerned with 'a themselves.
Eg: https://play.rust-lang.org/?version=nightly&mode=debug&editi... do_something_with doesn't need to have any lifetimes from the allocator.
If by Zig-style allocators you specifically mean type-erased allocators, as a way to not have to parameterize everything on A:Allocator, then yes the equivalent in Rust would be a &'a dyn Allocator that has an infectious 'a lifetime parameter instead. Given the choice between an infectious type parameter and infectious lifetime parameter I'd take the former.