Are the majority of humans reincarnated from the lower worlds? I read the following on the internet: 


  Birth as a human is extremely rare the majority of humans most likely
  came from hellish worlds, the animal realm, or the realm of ghosts
  prior to this human existence.....


Is it true or false according to the Pali suttas?
Teacher of the Devas: 


  In the round of samsara it is extremely rare to rise above the realms
  of woe, where the way out of suffering cannot be followed, and a human
  birth is even more favorable to awakening than birth in the realm of
  the gods.


Given that human life, because of its possibility for awakening, is even higher in terms of value to that of the devas, it would seem surprising in my opinion that the majority of humans come from lower realms where virtuous karma is very difficult to generate. 

The majority of humans, from a relative viewpoint, have had greater karma than the majority of sentient beings: 
The Nakhasikha Sutta says: 


  "In the same way, monks, few are the beings reborn among human beings. Far more are those reborn elsewhere [...]" 


Hence, even seemingly unfortunate individuals of the human realm have had a very fortunate rebirth, wherever they came from.

Also, there is a certain futility in speculating about karma, I believe, and the Buddha has somewhat suggested this in the Acintita Sutta:


  "There are these four unconjecturables that are not to be conjectured about, that would bring madness &amp; vexation to anyone who conjectured about them. Which four? [...] The [precise working out of the] results of kamma [...]"


Because rebirths may take different paths, and an individual may be reborn in the lower realms from lifetimes in the heavenly realms, or vice versa, there seems to be little meaning as to what realms human beings come from: they come from samsara. If a human being comes from the lower realm when they have spent infinite eons in every other realms, only a minute perspective would make their last rebirth significant; seeing the vastness of samsaric life, any specific rebirth is meaningless in the whole. My take is that such a minute analysis was what was reprimanded by the Buddha. Only a vast perspective gives a right impression. 

I mean, is there a meaning to a person reincarnating from heavenly realms to the hellish realms to a human birth, different from the hellish realms to the heavenly realms to a human birth? I don't see any. 

Now, relative to your exact question, 'Is the majority of humans from lower realms', there is the notion of different periods of time such as anatarakalpas, where different levels of fortune and virtue appears among human beings. If fortunate karma is different across time periods for humans, how could the same phenomenon of rebirth explain this? Do low points of human civilization and high points with the presence of Dhamma involve the same process of rebirth? Difficult to say. I think that Maitraya's time involving eighty-thousand years of life and the subsequent period where humans live ten much worse years may not have the same level of karmic fortune. 

All this to say that these considerations -- even without including the perspective of selflessness of phenomena -- suggest that the question is a difficult one.

Hope this helps!