Keep the motor runnin' may refer to a fast getaway, from, say, a bank robbery. The driver keeps the motor running so the robbers can jump in and speed away. It also has sexual inuendo, as in keeping up a sexual interest in something.
I've not heard of keeping the motor clean as a idiom, but it may suggest that a clean engine (human or mechanical) is more efficient. Perhaps clean means drug-free?
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