Who is Lola's mom in the New World? During the Thriller Bark Arc Lola mentioned to Luffy that her mother is in the New World and indicates that she is a extremely powerful pirate. She even left Luffy a vivre card that if ever he runs into any trouble he could ask her 'Mama' to help him out. 

Who could possibly be this extremely powerful pirate Lola's mother?
We know nothing about that as of this writing, but there has been a widely circulating theory for a while now that Big Mom is Lola's mom. You can read about it on various sites. I'll list a few points made in support of the argument on Reddit


  Firstly, for those that don't already know the theory, it is that Big Mom is Lola's mother. Back on Thriller Bark Lola gave Nami a vivre card with Lola's signature, saying her mother is a pirate in the New World. People believe this mother is Big Mom because:
  
  
  Big Mom's name is Big Mom, ie, she is known as a mother.
  Big Mom is in the New World
  Big Mom's jolly roger has big red lips and the same colour hair as Lola
  Nami who has Lola's vivre card just happens to be on the ship that is being attacked by the Big Mom pirates
  Nami is likely to eventually pull out the vivre card that Law gave her and accidentally pull out Lola's card instead.
  


Here is the similarity between Big Mom's jolly roger and Lola's face:


Another few points made in the Wikia are:


  
  Big Mom is in the New World and thats where Lola was born
  Lola's crew also said that her mother was an extremely powerful pirate which is another connection between the two
  Luffy will definitely meet Lola's mother on account that the crew was given her vivre card and it only makes sense that Luffy meets all members of the Yonkou
  


Lola's crew stating that Lola's mom is an amazing pirate:





Another popular theory recently is that her mom is Miss Bakkin

The arguments in support of these here are:


  
  Miss Bakkin is the first pirate woman to be introduce for a while and she is a mother which is really rare in One Piece, since all mothers are dead.
  Miss Bakkin and Lola have the same hair style, Weeble has the same type of hair braids, Lola’s mouth looks similar to that of Miss Bakkin. 
  Bakkin also claims to be Whitebeard’s lover, while Lola has been desperate to find a lover herself. Is she possibly trying to imitate her mother?
  The other connection to Lola is Thriller Bark itself. Lola’s reason for being in Thriller Bark could have been a search for Hogback. Maybe Weeble needed a doctor and they thought Dr. Hogback could help them. This would explain the stitches on his face, around his neck, and his arm.
  


Similarity between Lola, Miss Bakkin and Weeble:





Obviously, this is all speculation at this point and we won't know who her real mom is unless revealed by Oda himself. Although, based on these theories, it's likely that it's either going to be Big Mom or Miss Bakkin.