What did I write that suggests you wouldn’t get a deterministic specific sequence equivalent to a lock within the RNG? What I said is if you fail to synchronize the surrounding code’s order of calls into the RNG, then you’re going to have non-determinism anyway even with locks within the RNG.

For example:

    T1:
    If rng() < 0.5 {
       Rng()
    }

    T2:
    Rng()

The specific numbers returned by calls to rng() depend on the thread ordering UNLESS the user carefully has higher level synchronization themselves to guarantee the ordering. This shows that the locking within the RNG is insufficient and the better performing option that maintains equivalent invariants should be selected (i.e. initialize the TLS RNG state for the new thread from a call to read entropy from the current thread’s RNG state).