How long will a C# lock wait, and what if the code crashes during the lock?

When another thread comes by and wants to execute the code, how long will it wait until the lock is released?

lock will block the the thread trying to enter the lock indefinitely until the object being locked on is released.

can you somehow set a timeout?

If you need to specify a timeout, use Monitor.TryEnter as in

if(Monitor.TryEnter(obj, new TimeSpan(0, 0, 1))) {
    try {
        body 
    }
    finally {
        Monitor.Exit(obj);
    }
}

if the DoIt() method throws an exception, is the lock still released?

Yes, a lock(obj) { body } is translated to:

bool lockWasTaken = false;
var temp = obj;
try { Monitor.Enter(temp, ref lockWasTaken); { body } }
finally { if (lockWasTaken) Monitor.Exit(temp); }

For the gory details on what can happen when an exception is thrown, see Locks and exceptions do not mix.