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I don not know who Lola was going to marry but, I don't think Lola ran away from home because she did not like whoever she was going to marry. If we take BM words literally, Lola may have understood this and ran away, not because she hates her mother, but it could have been a great disaster. If you look at this page we see Luffy claiming BM is too dangerous to control Fishman Island, and that is true when we saw she destroyed a village for not providing enough sweets. It could be that Lola appreciated this and believed that the title of Pirate King would have been to0 great for someone like BM. Remember that Lola set off to sea to become a pirate herself, which may mean that she has a different viewpoint on piracy than her mothers.

I want to point out that I find it pretty interesting that BM has many children. As they constitute all the important roles in her organization and the use of hommies, this implies that BM inherently does not trust many out of her family, and she knows that her own children will come with a high level of loyalty and does not need to fear betrayal (also explains why she wants the Germa 66 technology). I honestly don't believe a lot of people trust her (aside from her family). I very much agree with Judge when he claimed she is deranged (http://www.mangareader.net/one-piece/833/21), and that accompanied by BM killing a loved one when someone misses her tea party, you can start to see that BM herself acknowledges her behavior and knows how others perceive her.
The one big hole in this theory is the whole BM/Lola connection, and what terms are they on.
I see two things are gonna happen:
1. Big Mom is gonna open the box and it explode and injure her
2. Luffy is gonna have the animals in the book as allies they will help him , who know how strong they are and Luffy is someone, who can understand and tame them and he can hear the voice of all things . all he has to do is taking Mondour down , that should be easy enough .
that is a way to take BM down.
Thanks for the spoilers! Sounds like an interesting chapter with a fair amount of plot progression and new insights!
Happy to see Bropper and Brook about to make their moves, I like their roles with being so important to the success of this arc.
The Lola situation is also getting more and more.. exciting?! I don't think Mama saying she would have gotten Pirate Queen with that marriage should be taken as absolute proof it would have been so easy, but I like the suggestion some made with her interest in Germa's technology and Caesars Giantification that Vegapunk might have played a role in that, or better yet: Giants themselves.
Speaking of Giants, this "hatred", or maybe it's a deep rooted "dissappointment" when Judge makes that observation gives another side to Big Mom's supposed dream of having her children turned giants. Giants seem to create the hole in Big Mom's utopia she still hasn't filled, and Lola having been in Thriller Bark with Oz the Giant connects nicely if her supposed groom had something to do with them ;)
