See the name "Dining Philosopher's Problem" is used intentionally , but you have to examine the code to check whether the properties of mutual exclusion , progress and bounded waiting is satisfied or not.So now let's discuss in light of the given code :
Let for the time being we do not use wait(lock) statement and here lock is a binary semaphore.Now let's see what happens.In light of the classical dining philosopher's problem , a solution to this can be considered as correct if a person can have both left and right chopsticks at the same time.
Now consider a scenario where wait(lock) is not used.Let the processes be P0 , P1 , ...P4..Let P0 execute wait(fork[0]) where fork[0] is also a binary semaphore.Now we preempt P0 and go to P1 , execute wait(fork[1]) . We repeat the same process till P4 executes wait(fork[4]).Now all of the processes have executed one wait() operation each of which are successful wait() operation.Now value of fork[i] = 0 for 0 <= i <= 4 since wait() has been performed on each fork[i].
Now when we try to execute wait(fork[(0+1) % 5]) for P0 which is wait([fork[1]) which is already held by P1.Similarly P1 tries to execute wait(fork[2]) but that is already held by P2.In short , no process is able to execute its 2nd wait() operation and hence no one can go into critical section and eat().In other words the processes are deadlocked.So this is not the correct solution.
Hence , the wait(lock) and signal(lock) is necessary.We consider the preemption in this case here , so wait(lock) is say performed by P0 then lock = 0 and hence other processes are not allowed to do wait(fork[i]) unless and until signal(lock) is performed by that particular process after which other process can enter and try to do wait(fork[i]) operation.
In short wait(lock) and signal(lock) are necessary hence they cannot be removed.
Hence option B) is correct.So in such questions , we should always go with implementation which is given in the question not simply name as it may lead us to wrong answers
Also one more point to add that preemption can be taken anywhere in the code if it is a concurrent process in order to check whether the code works fine , gives proper result or not.
I hope I have addressed your doubt.