-- I'm going to call a Strawman logical fallacy: the reactions of the doctors are based on perceived normality and unjustly supplement the integrity of the argument.
-- The inclusion of "luck" into the argument is risky. It's quite vulgar in the post-modern age to lay causality at the feet of Fortuna. Luck is a vulgar imposition of order that distorts anything nearing truthful causality.
-- I'm going to call False Dilemma on the bullets offered; you did not offer the fullest set of options based on the options you gave; I'm not asking for a realization of every potential, just for the "do differs" and "do not differs" to be more neatly dichotomized in more logical form.
. 
Ultimately the idea is great but not proven here: you cannot reasonably compare 1.) the causality leading up to the morality surrounding the prosecution of a doctor regarding negligence in surgery resulting in death to 2.) the inverted causality of winning the lottery. 1 and 2 are apples and oranges.

I suppose there may be some connection between luck and morality, however, I have not yet been able to assess just what that might be. This may comport roughly with the above comment by Mello Jello. If, for example, morality has some universal parameters, then it would not appear to depend upon a roll of the dice, spin of a roulette wheel or draw of the cards. Granted, there are some probability theorists who may dispute this on one level or another. People argue over the proven reality of evolution all the time and in many ways, just as they argue over science vs. religion. There are always points of dissent. This is reality. And consciousness.

I guess I just don't see the relationship between luck and circumstance. Luck is, I think, uncontrollable, whereas circumstance is based in part on choices we make. If I choose to chase down and attack someone who throws me a single digit salute because I did not move out of his way in traffic, I have created a problem based on circumstance. What ultimately happens only depends on luck, inasmuch as either he or I may suffer or die, because of my choice, based on the circumstance. Manslaughter and murder are, if memory serves, legal distinctions, often decided before juries who receive judicial advice. Such outcomes accrue according to particular rules of law, with plea-bargaining---truth and justice, notwithstanding. Plato and such were great, in their times. Now, maybe not so much. Philosophers beware!

I would choose option three from a pure practical standpoint. It makes sense that not everyone can win the lottery -- nobody would play if it was so. Regarding the doctors' illustration, there would be no way to figure out who performed malpractice. Moreover, if that was a viable option, like you stated, there would be little disincentive to perform malpractice.
From a philosophical standpoint I would also choose option three. Every lottery player knows what they are getting into when they buy a ticket -- they have a small chance of winning. They also know the next person in line has the same chance of winning. That means there is nothing unfair about either situation; each participant in your illustrations has the same chance of the said result.

You're absolutely right. I honestly felt overwhelmed by the argument and I wasn't sure if I should have even replied to it. But I did and it's blatantly obvious that I attacked the knot without the slightest idea of how to untie it. Next time I find myself in this position I will simply ask questions. I'm finding that sophistry is such an easy trap to fall into for beginners but I'm trying my hardest to be at least Socratic. The constructive criticism is much appreciated.

"Moral"; to defer to religious teachings...What are the creator's view of Moral Luck?
If someone accidently causes the death of another, the action was not intended to kill, but the consequence killed, the actor could flee to a city of refuge to escape judgment and punishment; therefore, intention matters. (Old Testement). If the lack of moral intention exists within a person which has them desire and intend to kill or commit other moral faults, they are as guilty as someone who has acted upon them... whether they acted or not; the character and intention matters.(New Testement- sermon on the mount, regarding adultery, lusting after a woman COMMITS adultery already within his heart).
Intention matters more than outcome.

I do not believe luck and circumstance are the same. I am not "surprised" by this belief, just as I am not surprised by my disbelief in "any" relationship between luck and morality. Luck is,as I have maintained, unpredictable. Which is why I, for one, do not play lotteries or slot machines. Circumstance is at least somewhat within our control: don't walk or jog in the street, at night, wearing black clothing, while listening to your favorite Black Sabbath tunes on your walkman---or whatever the current distractive device you might have acquired. Hopefully, these illustrations will clarify my beliefs---although I doubt it. Joggers, walkers and bicyclists die often in my state and city because they do not believe they should have to look out for themselves. This is a pity, but it due to irresponsibility,or: circumstance;... not luck. Why is it this is so difficult for people to understand? I AM surprised by stupidity---and baffled, in this age of reason and enlightenment. Or, it is?...hmmmmm.

There are at least 3 different threads here: 1. moral, 2. psychological , 3. legal.  Only the first is really the purview of philosophy.  My take, which I think is common, is that luck should not affect morality but does in fact affect psychology.  Assuming the latter is widely held, the legal realm should follow the psychological one or the laws will not be supported.

Let's start over and try to simplify this apparently complex discussion. Firstly, might we define morality? Oh, no! This won't do will it? Because morality appears to be CULTURALLY connected---examples include the manner in which negroes were treated in early America, and the manner in which women are treated in India today. But wait. Moral issues depend on where one lives? Yes! Surprise! Morality IS a function of culture, practice and tradition. Ergo, if we aspire to change morality, we must, therefore,aspire to alter the culture(s) that offend our notions of what is properly moral. This has not worked much in my short lifetime. Nor did it work in the short lifetimes of my parents. Say What You Know. Share What You Have. Do What You Can...Notice, then, I have dwelled on morality, diverse though it may be. Morality is a function of cultural intractibility. It is where we are more than who we BELIEVE ourselves to be. How quaint.
Now, to luck: Snake eyes, you lose; boxcars, you lose; play the lottery?---dice game odds are better, short-term---but, there is no morality to gambling. And you can take that to the bank. Heh, heh.
If any of the above reminds you of history, it should. You have lived it; if you noticed. As to the gambling observations, those are merely peripheral facts. Good night.
Harold.
(I'll consult with anyone on matters of cultural intractibility and Historionic Effect, but my time is valuable, therefore(or ergo), expensive.)

Here's another perspective.  Fairness is a strong human intuition, helpful in fostering social cooperation but sometimes felt inappropriately.  An doctor who doesn't check for diabetes before administering anesthesia risks not only the death of his patient but his job.  That's the upfront deal, which everybody understands.  If he takes a shortcut and gets away with it, he's been lucky and suffers no penalty.  If the patient has a seizure and dies, the doctor has been unlucky on two counts and takes the consequences.  A losing $100000 bet on the stock market might cost one guy his home, while another has only to postpone the purchase of his new sail boat .  The consequences of the potential loss have to be factored in to the decision to make the play, in which case there is no unfairness in the outcome.
Hugh

Well-stated, Hugh---well-stated. I live as practically as possible. Sounds like you do too.
Newman.

"What one deserves should depend on one?s own intentions, desires, motivations and things like that; it shouldn?t be a matter of...x."
What one deserves, in terms of reward and burden, very much partly depends on the effects which one's actions have on others of equally well-intentioned moral standing. If my physiology needs the thermostat turned up and yours needs it turned down, we each could be wrong upon the other in our own good intention to 'make the world the right temperature'.