I had a theory about Lola and Chiffon replacing each other with the help of Pudding's power, but let's set that aside for a minute, because my brain just broke.
Lola and Chiffon are the 21st and 22nd or the 22nd and 23rd children in the family. Based on Prospero (the eldest son) and Brulee (the eldest daughter we've seen so far) appearing to be in their late 50's - early 60's, We can assume that Lola and Chiffon are in their late 30's - Mid 40's.
An indeterminate number of years ago, she ran away from an arranged marriage that would have made Big Mom (or gotten her closer to becoming) the Pirate King.
Based on Pudding's flashback panel with Lola, she looked to be in her late teens, probably around 18-19.
So, let's assume that Lola is 44 now. If she was 18 when she left Totto Land, that was 26 years ago.
26 years ago was the year Roger was on the way to becoming Pirate King. This was also roughly 2 years before Ace was conceived.
An indeterminate period of time ago, Big Mom made a "Mistake" in dealing with Roger that allowed him to get the Road Poneglyph info and continue to Raftel.
A "Mistake" was made that allowed Roger access to a very well guarded treasure of Big Mom's. In general, Totto Land is very highly patrolled and would be certain death for anyone attempting to enter uninvited unless they had a direct route, like the Sanji rescue crew did.
Roger would need access to Whole Cake Chateau (and the Poneglyph) through other means than a direct assault.
A Marriage was planned to form an alliance that would give Big Mom enough power to declare herself "Pirate King".
As has been shown, Married family members and their crews/vassals are allowed free access to Whole Cake Island (The Firetank Pirates, the entire Germa Kingdom).
So, what if... Roger pretended to agree to Marry Lola?