Is the answer dealing with a case where it is probably a lemon, and you are obligating him not to follow the majority in commandments but rather to be concerned for the minority possibility that it is an etrog and therefore to take it? I’m not sure I understood.

Sorry, I got confused (I thought the case was that it was most likely an etrog). Here too we follow the majority, and therefore one should not take it with a blessing. If he wants to take it without a blessing he of course may, but certainly there is no compulsion.
Even in a perfectly balanced doubt, in such a case there are opinions among later authorities that one is not obligated to take it in these circumstances. This is like the doubt regarding tekhelet, where in the Radziner Rebbe’s book he cites Rabbi Akiva Eiger that there is no obligation to be stringent where it is not certain that he will thereby fulfill his obligation. Rabbi Akiva Eiger’s argument is that the obligation to be stringent in a Torah-level doubt applies only when the stringency will remove him from the doubt. For example, in a case of doubt whether something is prohibited pork, if you do not eat it then you certainly have not transgressed a prohibition. In such a case you must be stringent. But in a case of doubt whether this is tekhelet or not, even if you are stringent it is still not certain that you fulfilled the obligation of tekhelet, and therefore in such a case there is no obligation to be stringent. And so too here, of course.
This is not necessarily a distinction between a positive commandment and a prohibition, as some have understood. There are cases of a positive commandment where one must be stringent even according to Rabbi Akiva Eiger. For example, in a doubt whether there is an olive-sized amount on Sukkot, one must be stringent and eat in the sukkah, because if it is less than an olive-sized amount then there is no obligation upon him at all. And so too in other similar cases.

According to that reasoning, since he would still remain in doubt, there is room to ask: what if after taking the minority possibility into account he would know whether he succeeded—would he be obligated to try? For example, there is an etrog locked in a box, and he has a key in his pocket that is probably not the right key. Is he obligated to try opening the box with the key and attempt to get the etrog? That it is proper and good and admirable is obvious, but is he obligated? And do we compel him?

When it is an even doubt—yes. When it is only a minority possibility—no. I didn’t understand the example.

The example is that there is definitely an etrog beyond the door, and the odds are that even if he goes to open it he will not succeed in opening it and taking the etrog. Is the Rabbi saying that he has no obligation to go and try to open it? The added element in this example is that after he tries he will leave the state of doubt: either he will know for certain that he was prevented by circumstances beyond his control and is exempt, or he will know for certain that he fulfilled the commandment of etrog.

That is no different at all from the doubt regarding tekhelet.