If a program is lock-free, it basically means that at least one of its threads is guaranteed to make progress over an arbitrary period of time. If a program deadlocks, none of its threads (and therefore the program as a whole) cannot make progress – we can say it’s not lock-free. Since lock-free programs are guaranteed to make progress, they are guaranteed to complete (assuming finite execution without exceptions).
Wait-free is a stronger condition which means that every thread is guaranteed to make progress over an arbitrary period of time, regardless of the timing/ordering of thread execution; and so we can say that the threads finish independently. All wait-free programs are lock-free.
I don’t know offhand of any Java examples which illustrate this but I can tell you that lock-free/wait-free programs are typically implemented without locks, using low-level primitives such as CAS instructions.