This is fairly close to an XY problem. That is, the question being asked is essentially how to mutate a captured local variable from a lambda. But the actual task at hand is how to number the elements of a list.
In my experience, upward of 80% of the time there is a question of how to mutate a captured local from within a lambda, there's a better way to proceed. Usually this involves reduction, but in this case the technique of running a stream over the list indexes applies well:
IntStream.range(0, list.size())
.forEach(i -> list.get(i).setOrdinal(i));