Unlike deadlock and livelock situations, the threads in a lock convoy do progress; however, each time a thread attempts to acquire the lock and fails, it relinquishes the remainder of its scheduling quantum and forces a context switch.
The passage describes how threads within a lock convoy operate differently from deadlock or livelock situations.  While they continue to advance, each time a thread fails to acquire the lock, it gives up its remaining time slice and forces a system switch.