Thanks, but I'm not questioning that they're both perfectly fine English phrases.
However - don't they have a slight difference in meaning?
"Can you take me to the station?" meaning "Can you please get your car keys, start the car, drop me off at the station and then go home again?" vs.
"Can you give me a lift to the station" with the *additional* meaning - "As you're going to the station anyway on some other business /As you're going past the station with your car anyway, can I please come along?"
i. e. - "give a lift" just meaning "take somebody as a passenger on a trip that would be taking place anyway" (which is the idea of "mitnehmen").
Or have I been using the phrase wrong my entire life?