When something is much more likely to happen some way than the another you can call it luck when it happens but its really just turning out the most likely way. In sports a stronger team beating the weaker is usually not described as luck - its just how it was supposed to be. Even if the weaker could have won also.
Also describing as luck that you have alternate way to India is... Geography is not luck. If Europe had the climate to grew spices they would never have developed the navy to travel to India. Because they wouldnt have needed to. If Arabia was water they wouldnt need to travel around Africa and again they wouldnt need to develope better ships and sailing methods. But thats not luck according to you. Its only luck if the europeans come out on top. Thus you can conclude that the europeans were extremly lucky. In reality they had just much better motivation to explore and develope their navies than the rest of the world. And when as a result they found they had naval dominance they used that to get as much money (mostly through trade) as possible. In the process they ended up conquering most of the world.
And if the result of something (Europe vs locals) is consistently the same its not luck. No one is that lucky.
Also you can continue to repeat your points - that doesnt make them less ridicolous. Blaming everything on European luck from geography to the biology of the natives... And the cherry on top is the "Christianity existing to unite Europe" part - which of course is agan luck according to you. Its not like the christianosation of europe was a centuries long process with a thousand causes - but here its simple luck. Also of its supposed unity: 30 years war? Just to mention the most devastating war thanks to christian infighting. If thats your definition of unity I dont want any of it.
I want to point just to the central idea of 1st paragraph.
Saying that something more likely to happen cannot be based on luck, but on cause-and-effect is obviously right.
But how can we tell the world as we know is the most probable outcome of all possible outcomes of events many centuries ago?
In statistics, to make an inference about the probabilities of different outcomes of some event we need a sample of hundreds. In History we have a sample of just one event: our actual World History.
Surely when we see European armies usually defeating native ones so many times we can call it a good sample and make the statement: "when the Europeans fight the natives an European victory is the most likely outcome".
But it is due to technological and tactical advantages. The true question is: "what is the probability Europe will have tech advantage"? Or: "what is the probability Europe will pursue trade routes to East Asia" (instead of Chinese and Indian countries pursuing themselves maritine routes for their ships selling directly in Europe).
This kind of questions cannot be answered at all. Because we can only see our actual World and not a multiverse of different parallel Worlds as in some sci-fi books.
Many people here seem to have a Jared Diamond-like thinking. No problem with it, but taking that not as an explanation for actual World, but as an explanation of the most probable outcomes of different alternate Worlds is a step from biological and geographical determinism.