(Can I) give you a lift?
Can I drive you to some destination? I'm driving that way. Can I give you a lift?
(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.