How do you implement a timeout on acquiring a lock, and why would you?

synchronized has no timed acquisition at all: you wait forever or not at all. tryLock(time, unit) returns a boolean, and that boolean is the whole point. It turns a potential deadlock into a failed operation you can retry, log or fail fast on.

if (!lock.tryLock(500, MILLISECONDS)) {
    throw new TimeoutException("could not acquire " + name);
}
try { ... } finally { lock.unlock(); }

The classic use is locking two accounts for a transfer: take the first, tryLock the second, and if it fails release the first, back off a random amount and retry. That breaks the hold-and-wait condition, so the deadlock cannot form. Note the bug people write here: calling unlock() in a finally when tryLock returned false throws IllegalMonitorStateException.