I don't think a critical section is necessarily related to parallelism, but concurrency (As shown in other examples in this thread). If you google for "critical section", the first link (Wikipedia) begins "In concurrent programming,".

Regardless, if you were to have need of a lock, which was the basis of this chain of comments unless I'm missremembering, a read-write lock could improve performance, regardless of things being singlel threaded, precisely because of things being async (If you have N async tasks all read-only locking an rwlock, they can go on to fire async requests, which will run concurrently, despite the execution being single threaded).