Ensure Java synchronized locks are taken in order?

No you cannot be sure that two calls to a synchronized method will occur in order. The order is unspecified and implementation dependent.

This is defined in the 17.1 Locks section of the JLS. Notice that is says nothing about the order in which threads waiting on a lock should gain access.

No, synchronized will give access in any order (Depends on the JVM implementation). This could even cause Threads to starve in some scenarios.

You can ensure the order by using ReentrantLock (since Java 5.0) with the fair=true option. (Lock lock = new ReentrantLock(true);)