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Phrase(s): (Could I) give you a lift?
Can I offer you a ride to some place? (Also used with can or may in place of could.) • Bill stopped his car at the side of the road where Tom stood. "Can I give you a lift?" asked Bill. • John: Well, I’ve got to leave. Alice: Me, too. John: Give you a lift? Alice: Sure. Thanks.
McGrawhill's American Idioms And Phrasal Verbs