The Survival Lottery

When two or more patients who would otherwise die can be saved by a transplant from one donor and no 'natural' donor is available, a computer is to randomly select a donor to 'give life' to the patients by giving up his own.

Is the Survival Lottery morally acceptable?
A Misguided Response:
The Survival Lottery is unworkable.
Transplants need to be done too quickly for the system to work properly.

The system could never be made tamper-proof.

etc.

But these objections just avoid the hard moral question.  What if you could run the system effectively?
A Common Response:
'This shows you what's wrong with Utilitarian thinking.  Some lines can never be crossed no matter how much good crossing the line might do.'

Is this correct?

What if you could save 1,000 people by killing one innocent person? 100,000? 1,000,000?
When push comes to shove, what matters:  principles or results?
[Philosophy 1200]