Wouldn’t blue loctite on something the size of a lockring be really hard to undo?
I think it’s closest to a threaded bottom bracket or a cassette, therefore I’d use copperslip or grease if I didn’t have any.
Most BB’s come with loctite pre-applied, you can always go with green loctite if you’re worried about un-doing it.
Neither are required for a lock ring that requires 40Nm of torque to secure.
But really this is the answer.
The only things I bother to re-apply loctite to are suspension pivots and the axles/adapters on hubs where they screw together. Most other bits are either torqued up tight enough that they’re going nowhere, or not loaded in ways that would tend to loosen them.