According to e. j. lemmon distinction between a platonic and a sartrean dilemma
E.J. Lemmon understood moral dilemmas as cases in which an agent both ought and ought not to do the same thing. Specifically, he claims an ought statement may be based on a person's duties, on his previous commitments, or on general moral principles. A moral dilemma can arise between a principle and an obligation. This is illustrated with the Platonic case of returning a weapon to a mad friend. In this dilemma, one's imperatives are clear and they conflict. In Lemmon's second example of a moral dilemma, the Sartrean case, one has "some, but no conclusive evidence" that one ought to behave in a certain way. "Part of the very dilemma is just one's uncertainty as to one's actual moral situation" and this moral uncertainty exacerbates the dilemma and makes it "dilemmatic in the full sense". Our understanding of moral dilemmas if affected by both of these illustrations as they are both resolved in different ways.
The distinction between a Platonic and Sartrean dilemma lies within the idea that in the Sartrean case, we lack a clear picture of the options, unlike in the Platonic one where it is apparent that we ought or ought not to do something. The Platonic case is as follows: A friend leaves you with his gun, which you promise to return to him when he calls back later. He arrives back in a distressed state and demands his gun, announcing that he is going to use it to shoot his wife as she has been unfaithful. You ought to return the gun as you promised to do so, and yet you ought not to do so as you would be indirectly responsible for murder. As Lemmon has said, you are "in an extremely straightforward moral dilemma, evidently resolved by not returning the gun". In order to further demonstrate this example as a dilemma, Lemmon considers the features of what he calls "the logic of modal verbs". He states that it may appear to be contradictory that a man both ought and ought not to do something, however he clarifies we should not regard "ought" and "ought not" as contradictories. The logic of "ought" is an important point in furthering our understanding of moral dilemmas as it enables Lemmon to show something about the sources of dilemmas. Both sides of a moral dilemma, whether it is of the form "ought" or "ought not" is supported by a different kind of moral consideration. Thus you ought to return the gun because you put yourself under an obligation, but you ought not to return the gun because of a moral principle. The Platonic case, therefore, is a clear example of a conflict between principle and obligation.
How we resolve this dilemma affects our understanding of moral dilemmas more generally. With the Platonic case, even a failure to make a decision counts as a decision. By avoiding a decision, we are doing something which we ought not to do, and so can be called upon to justify either our activity or inactivity. The only way we can avoid a decision is by ceasing to be an agent. So Lemmon suggests that someone in a moral dilemma might consult others in order to resolve their predicament, but he thinks this is likely to be indecisive. His point is that such moral advice would only work if the agent in the dilemma took on this advice as part of their own moral outlook. If this happens, and the advice made one course of action the obviously right one, then the dilemma would simply disappear. This, however, is problematic as if the dilemma was able to be resolved; this suggests dilemmas are in general not real. One could therefore argue that the Platonic case cannot be described as a genuine moral dilemma. For the agent's solution in that case is clear; it is more important to protect people from harm than to return a borrowed weapon. And in any case, the borrowed item can be returned later, when the owner no longer poses a threat to others. Thus in this case you could say that the requirement to protect others from serious harm overrides the requirement to repay one's debts by returning a borrowed item when its owner so demands. When one of the conflicting requirements overrides the other, we do not have a genuine moral dilemma. Whilst Lemmon is insistent that moral dilemmas do occur, there appears to be a genuine reason to accept that the Platonic one is not a real dilemma at all.
What differentiates the Platonic case from the Sartrean one is this: in the Platonic one, we know what our obligations, duties and principles demand of us even though they conflict, whereas in the Sartrean case we do not even know that much. The second dilemma Lemmon puts forward is the Sartrean case of the student who does not know whether he should join the Free French Forces or remain with his mother. He thinks it is his duty to fight, "but can it really be his duty, given his obligation to his mother," Lemmon asks. The boy is unclear where his duty lies partly because he is unclear what exactly would be the outcome of his decision to leave his mother, and this outcome is also relevant to the decision itself, as a utilitarian consideration affecting his choice. The concept of responsibility also adds another dimension to complicate the student's choice. Whatever course of action he takes, it seems likely that the responsibilities that will result from this will create further difficulties as the choice he must make requires him to give one of those responsibilities priority. In the light of his responsibilities to his mother, the man must not join the resistance forces. But in the light of his responsibilities to his country, he must join the resistance. However he chooses, he will fulfil one set of responsibilities to the exclusion of the other. In such a dilemma, you do not know what morality requires of you, though you do recognise that whatever it is, it is bound to involve conflict of your responsibilities and duties.
The Sartrean dilemma further differs from the Platonic one in how it affects our understanding of moral dilemmas as Sartre portrays a dilemma which is clearly irresolvable, in which the agent must decide by himself and for himself, his course of action, whereas the Platonic dilemma can be resolved. We can take from the Platonic dilemma that in order to have a genuine moral dilemma it must be true that neither of the conflicting requirements is overridden. It is less obvious in Sartre's case that one of the requirements overrides the other. You could say that the agent's uncertainty about what to do in this case is simply the result of uncertainty about the consequences. If the student were certain he could make a difference in defeating the Germans, the obligation to join the military would prevail. But if the student made little difference whatsoever in that cause, then his obligation to tend to his mother's needs would take precedence, since there he is virtually certain to be helpful. The Sartre's case demonstrates that nothing can provide us with a solution to the student's dilemma. Whilst Plato's dilemma is resolvable, Sartre portrays a dilemma to which no rational solution can be offered.