You don't....
Why do you need a computer to land the moon mission (I'm not talking about the Apollo but a hypothetical moon mission)?

To address that question literally - Apollo 11's Lunar Module was manually landed when Armstrong took over control due to problems with the computer! Armstrong also correctly eyeballed range using landmarks (as the computer calculated vs radar values were reporting different, IIRC).
Also, an unmanned test (Apollo 5? first LM test, IIRC) ground control had to disable the on-board computer and finish the test remotely without the use of the onboard system (as it faulted probably due to bad human inputs related to test specific fuel aspects).
IC based onboard computers were not required, but rather were simply chosen over other options. Apollo was no miracle of chance technologies. Basically, politicians supported it and people managed to get it done before politicians could kill it, is all.