What makes a great a spiritual leader? Is it nature or nurture or something else? Two premises presumed for my question: 


The 14th Dalai Lama is an especially sincere spirit 
Reincarnation, beyond the scientific eg recycling of atoms / culture / dna, is an incorrect idea.


Is the 14h Dalai Lama's charisma created by being raised as a spiritual leader? Are all Tibetans especially sweet souls? Is it both or neither, but rather great luck?

I am trying to tease out nature &amp; nurture, and squeeze out the supernatural!
Notwithstanding your (questionable) second premise ... :)

I'll say that not all Tibetans are such sweet souls and you'd be hard pressed to find many that are anywhere near as incomparable as HHDL... but the answer is simple: practice of the Dharma.

His Holiness is a Bodhisattva who has been wholeheartedly practicing according to the Bodhisattvacaryāvatāra
 for many, many, many years if not many, many, many lifetimes. What you are seeing is the result of such continued and amazing practice. Consider his Holiness's favorite quote which he repeats constantly during his teachings:


  With a wish to free all beings I shall always go for refuge to the
  Buddha, Dharma and Sangha until I reach full enlightenment.
  
  Enthused by wisdom and compassion, today in the Buddha’s presence I
  generate the Mind for Full Awakening for the benefit of all sentient
  beings.
  
  As long as space endures, as long as sentient being remain, until then, may I too remain and dispel the miseries of the world.


If one faithfully practices and generates this Mind of Enlightenment the results will follow. You are just observing the results.