Normally, the word "like" is used when you compare nouns and "as" is used for comparing verbs. "He thinks like a lawyer" is normal English usage because no verb follows lawyer, so we have a parallel between "he" and "lawyer." "Law students learn to think as a lawyer does" is grammatically correct, though a bit unidiomatic. We--at least in the US--are more likely to say "Law students learn to think the way a lawyer does." A somewhat more subtle distinction follows: "As your lawyer, I advise you not to do that." This means that I am your lawyer and I'm telling you not to do it. "Like your lawyer, I advise you not to do that." That means that I am giving you the same advice your lawyer gives you. (I am like your lawyer in this case.)

You are perhaps correct from a strict grammar point of view. But I think it is deliberately written like this, as I have heard this sort of phrasing before, and to me the meaning is very clear. "Do as he says, not as he does." http://www.dailymail.co.uk/news/article-2565477/Do-says-not-does-New-York-mayor-Bill-deBlasio-caught-jaywalking-24-hours-speeding-blowing-stop-signs.html From the bible: He sees the Father doing; for whatever the Father does, these things the Son also does in like manner

Correct.. but in real life it's never a problem. Now, there is a significant difference between "he works like a doctor" and "he works as a doctor."

both are correct, it is simply your choice, but A sounds like a complete sentence B does not, it needs something to be stand alone like: A Law student must learn to think like a lawyer