Lock free doesn't solve this. One thread will always make progress, but you have no way to ensure it is your thread so you can miss a deadline with lock free. When the data is under a lot of contention across many cores this is an issue (most of us don't have hundreds of cores so we don't see this).

Generally lock-free is better for these situations as odds are when you hold a lock at least some CPU cycles are used for something that isn't directly modifying the data that needs the lock - those cycles the other CPU can touch it when lock-free. (note that when using a lock there is a trade-off, often it is better to hold the lock for longer than needed instead of dropping, doing a couple operations and then locking again)