"Lifeboat" scenarios are the most apparent example that immediately come to my mind.
Assume that you are stranded in a lifeboat with several others after having survived a plane crash in the Pacific, during a severe storm that had caused your plane to veer wildly off course (i.e., the "Cast Away" scenario).
Further assume that there are no rowing implements, and all navigational equipment washed overboard shortly after the lifeboat inflated.
Further assume that the supply of drinking water and food is extremely limited on the lifeboat.
Finally, assume that after having waited in vain many days for rescue, it has become apparent that the drinking water and food supply is insufficient to allow everyone on board to survive, and in fact that if the supply continues to be rationed among all of the lifeboat members, there is a significant likelihood that all aboard will die...since the supply is insufficient to provide a minimally adequate level of hydration, there is a significant probability that with continued equal rations, all aboard will be weakened too greatly to survive.
However, if one or more of the lifeboat occupants is killed, the survival chances of the remaining lifeboat occupants increase appreciably...not only will the food and water supply last longer, the blood (though salty) and urine of the victim can be drunk.
In that instance, do you cast lots and kill the unlucky occupant(s)?
Humans have faced these types of situations before. The Donner Party and Andes plane crash survivors both cannibalized the dead, although neither party endured the water shortage problem posed in the hypothetical above, and certainly the Andes party survivors were not forced to kill any of the people they ate...however, there is some evidence to suggest that some members of the Donner Party did cast lots to see who would be killed and cannibalized.
I suppose it could be argued that by agreeing to cast lots, each person is "purchasing" a fractional interest in wanting to kill each of the other members...but then again, assuming you've drawn a lucky lot, you don't want to kill anyone other than the unlucky person, and the unlucky person has consented to be killed, so he or she is not really trying to take your life.
Also, though I have never heard of a real-life instance of this, I watched the movie "Vertical Limit", in which rock climbers were faced with the prospect of cutting someone tethered below them from the line when the line anchor was too weak to support all of the climbers after a fall.
I suppose in that instance it could also be argued that the person being cut loose was also "trying" to kill you, since by his or her very survival instinct your life was also threatened.
But I think that PB's original question revolved around a more narrow definition of intent.