Why did Jesus tell the lepers he healed to go show themselves to the priests?
Because the law required it. Under the law, a person healed of leprosy had to present himself to the priests, who would then grant permission to re-enter society. Christ's earthly ministry operated entirely under the law with Israel, so He directed healed lepers to obey that legal requirement.
Les teaches that during Christ's earthly ministry there was nothing of the church and no church language. Christ was dealing under the law with the Jew under the law, constantly making clear that everything was still under the law. No word was said that temple worship or the commandments no longer had to be kept. So when He healed lepers, He told them to present themselves to the priests because the law demanded that a healed leper be examined by the priests, who would give permission to come back into society. The rich young ruler likewise was told to keep the commandments, and even in early Acts the twelve apostles were still meeting at the temple because the law was still in force.