Since you introduced the LUCA hypothesis that is cumbersome in its self, then you would have to go beyond your understanding to view all relevancy to it. The miller experiment is one, however just like everything scientific, it can be disproved by your own science, as in this case.
Previously my own, now this is Copy/Past so, not to have your audience think that my hypothesis is one sided as it has become the norm in this thread. What has this to do with the original question posted? Nothing, this goes beyond simple intellect and the posted question.
One textbook, edited by Soper (“Biological Science 1 and 2”; 3rd edition; Cambridge University Press) summarizes the situation well (p. 883):
Despite the simplified account given above, the problem of the origin(s) of life remains. All that has been outlined is speculation and, despite tremendous advances in biochemistry, answers to the problem remain hypothetical. … Details of the transition from complex non-living materials to simple living organisms remain a mystery.
This conclusion is echoed by those who have spent many years researching in
this field of biochemistry. Dr D E Hull wrote,
The conclusion from these arguments presents the most serious obstacle, if indeed it is not fatal, to the theory of spontaneous generation.
Prof Francis Crick, who was a great believer in the accidental origin of life
on Earth, said, “The origin of life appears to be almost a miracle, so many are
the conditions that had to be satisfied to get it going.” Prof.
Crick goes on to argue that this might be overcome in long periods of
time. However,
there is no justification for believing that time can overcome basic chemical
laws.
Dr H P Yockey (in the Journal of
Theoretical Biology, 1981, 91, 26-29) wrote,
You must conclude that no valid scientific explanation of life exists at present… Since science has not the vaguest idea how life originated on earth, it would be honest to admit this to students, the agencies funding research and the public.
