"וְלִפְנֵ֣י עִוֵּ֔ר לֹ֥א תִתֵּ֖ן מִכְשֹׁ֑ל" (Do not put a stumbling block in front of a blind person.)This seems to be a unique verse in the Torah, as the simple meaning of the words are not at all the meaning of this statement. In fact, suppose someone actually puts a stumbling block in front of a blind person. We may not give him shishi (or even, nebach chamishi) on Shabbos, but he has not violated a Torah offense. If the blind person actually stumbles and suffers damages, of course, he is obligated to pay those damages; that's a separate matter.
-- Vayikra 19:14
What the verse does mean, though (as Rashi notes), is that one is not allowed to give misleading advice to a Jew who has no insight into the issue at hand. For example, a life insurance salesman has two different policies to sell and he makes a larger commision on one of them. If he encourages his clients to buy the policy that make more money for him -- even though the other policy would actually be better for the client -- then the salesman is transgressing the issur d'oraisa of lifnei iver lo si'tein michshol. That's obvious, but there are more subtle examples also.
Suppose a storekeeper is known to overcharge by more than a sixth; he is certainly not allowed to to do that, but that's the situation. You need something that he carries and his is the closest store. You need the gizzy right now and don't feel like going across town to save 47 cents, so you are 100% mochel b'leiv malei his overcharges. Even so, you shouldn't patronize his store because you are encouraging him to continue his evil ways; thus transgressing lifnei iver. R' Moshe says that rosh yeshivos have to be on guard; if a talmid comes to his rosh yeshivah to discuss leaving, the rosh yeshiva needs to be certain he is giving advice that is best for the talmid rather than best for the yeshiva.
Now we come to doctors on Shabbos. Suppose a person needs to go to the hospital on Shabbos and has has a choice to use either a frum or non-frum (but Jewish, obviously) doctor. The two doctors are the best in their field and are equally competent. In that case it is better to use the frum doctor. The frum doctor will be doing a mitzvah of piku'ach nefesh and v'chai ba'hem; he therefore has permission to violate Shabbos. Regarding the non-frum doctor, though, the Beis haLeivi says that since he has no regard for Shabbos anyway and he is only going for his parnassa, he therefore has not permission to violate the Shabbos. In shamayim he will be charged with the same crime of violating Shabbos whether it is for a mitzvah or not; when we have the Sanhedrin (may it be soon and in our days), he would be chayiv misa. Therefore to ask the non-frum doctor is a violation of lifnei iver.
If the non-frum doctor is better, of course, then the patient can and should ask him. The lifnei iver violation does not preclude him for seeking the best medical attention for his condition. Suppose, though, that they are equally competent, but the patient thinks that using a non-frum doctor is better because he fears the frum doctor will be so concerned about Shabbos that he'll compromise the treatment. In that case (assuming it is his own mishagos), then the patient would be transgressing lifnei iver to call the non-frum doctor. Interestingly, suppose the frum doctor says, "Call the non-frum guy, I feel like spending Shabbos with my family." In that case, the frum doctor is transgressing lifnei iver.
R' Fuerst commented on that last case, "Being a doctor is almost as bad as being a Rav; when you get a knock on the door at 3:30AM, you have to answer it."