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1. Of a path or route, to continue or end up at some higher point or location. This trail should lead up to the peak of the mountain. That's the highway leading up to New York.
2. To help someone or an animal physically ascend some pathway or route. In this usage, a noun or pronoun is used between "lead" and "down." I led my grandmother up the stairs to her bedroom after supper. He held the frightened animal's harness and led it up the steep hill.
3. To guide or direct someone or an animal upward or to a higher point or location. In this usage, a noun or pronoun is used between "lead" and "down." Please lead our guests up to the veranda for some hors d'oeuvres. We'll need to lead the herd up to the fields above so they can continue grazing.
lead someone up something
to guide someone upward along some route. Would you please lead Tom up the path so he can leave his things at the cabin on the hill? Mary led the visitors up the stairs to the loft, which she had recently redecorated.