As with all I/O, you have little choice but mutual exclusion. You may theoretically build up a complex scheme with a lock-free queue which accumulates logging entries, but its utility, and especially its reliability, would be very questionable: without careful design you could get a logging-caused OOME, have the application hang on due to threads which you didn't clean up, etc.
Keep in mind that, assuming you are using buffered I/O, you already have an equivalent of a queue, minimizing the time spent occupying the lock.