Final answer:
The man escaped punishment by presenting a paradoxical statement that neither could be proved true nor false without causing a contradiction, thus the King had to let him go.
Step-by-step explanation:
The paradoxical statement the man must have made to save himself is "I will be killed by trampling of wild buffalo." This statement presents a logical paradox. If the statement is true, then according to the King's rule, the man should be killed by lions. However, being killed by lions would make the statement false. Conversely, if the statement is false, he should be killed by trampling of wild buffalo, which would in turn make it true. This paradox forces the King to let the man go, as neither form of execution could logically proceed without contradicting the conditions set by the King.