How did Jonathan's son Mephibosheth become lame?

Answer: He fell as his nurse fled

When news came that Saul and Jonathan were dead, his nurse fled with the five-year-old; he fell and became lame.

“And Jonathan son of Saul had a son who was lame in his feet. He was five years old when the report about Saul and Jonathan came from Jezreel. His nurse picked him up and fled, but as she was hurrying to escape, he fell and became lame. His name was Mephibosheth.”— 2 Samuel 4:4 (BSB)