As usual, we won't come up with an exact translation for it.
I like all the suggestions. "To give st a lick and a promise" sounded to me more like the soldier overseas who is telling his native lady "I will come back for you".
The meaning of "ser la ley del mínimo esfuezo" regarding a student means the student is indeed a bump on a log who every now and then shakes off their usual apathetic disposition just to get the minimum "momentum" to achieve a C minus and "survive", with "mínimo esfuerzo" meaning here just enough to avoid dire consequences from an academic standpoint and "ley" meaning it to be systematically done.
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