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Above piece of code will not work on any system. following is the reason:

-> Single Processor : Lets assume Thread1 executes first line and found that "lock = 0" so it will go in to else condition. Before executing "lock =1" statement task switching takes place and another thread2 also found that "lock = 0". Thus at the same time 2 threads are in their critical section.

-> Multiprocessor system : Assume that 2 threads are executing same piece of code in parallel and both of them found that "lock =0" so both threads will enter into critical section.

Thus above code will not work on any system.

Issue:
wait() will not work.

Root Cause: :
wait() (and notify()) work on resources\objects not on threads. But in this piece of code you are calling wait() on this (thread instance) not on object\resource.

Solution:
In place of static int variable use a Object as a lock:
private static final Object lock = new Object();

wait() -> lock.wait();

synchronized (lock) {
	lock.wait(); // It's already locked so wait(sleep) till someone wakes me up 
	try{
		/* Critical Section - Increment g */
	}finally{
		lock.notify();
	}
}

This is not specific to java..Its a general block of code

the lock itself is not thread safe, will not work in any system.

The waked thread doesn't lock the lock before entering the critical section.

first problem:
if one of the thread dies without unlocking no one can lock the resource again.
Second problem:
Only one thread can lock the resource at any point of time. Something like binary semaphore even on a multiprocessor system i.e. this code doesn't utilizes the mutlicore architecture.
As of now i can see only these two but i am sure there are many more.

The code will not work on any system. "if" should be replaced by "while" for the lock to serve its purpose.

* Time taken to execute lock can cause problems. Two or more threads can execute lock at same time. Better solutions is to use condition variables with mutex locks.

To be precise, answer should be "it may work sometime and fail sometime"
Explanation:-
We have two processes P1 and P2, and lock=0;
if (lock) ---- Line 1
wait(); // It's already locked so wait(sleep) till someone wakes me up --- Line2
else ------ Line 3
lock=1; // I locked it ------ Line 4
/* Critical Section - Increment g */

lock = 0; // Lock released, so wakeup only one of other waiting threads, if any

Let's say P1 is scheduled first, and it execute Line1, and context switched with P2, and again P2 executes Line1, now we arrived to the condition where both P1 and P2 see lock as free, and will execute Line4, and as a result there will be deadlock as both will wait for lock to be freed but none would be able to do so.

It depends upon the scheduler.. To avoid this dependency we have to ensure that the lock value assignment is an atomic operation ..after that it will work fine in any conditions

ash04 and others are right. This will NOT work. For those who mention working sometimes I have a financial program for you to use. Half the time it puts your paycheck in your bank account and the other half it puts it in mine ;-)