I would suggest that you pick one term for her grandmother and use it as a proper Name for her from the MC's point of view. Similar to how one might call a female parent Mom despite the real name. IRL, my father's parents both divorced and remarried before I was born, and while I had 3 sets of grandparents, I would use different names to refer to each: PopPop and MomMom (Paternal grandfather and 2nd wife), Granny and Granddad (Paternal grandmother and 2nd Husband), and Grandma and Grandpa (maternal grandparents).
Similarly, it's possible that your character would refer to this grandparent as "Abuelita" or "Abuela" when discussing that specific woman or talking to that woman, but would refer to their relationship as "grandmother/grandparent and grandchild/grandkid."
Gramatically your example needs work. The word "mami" should be capitalized as it refers to a specific individual (a mother) by a common term for a person of that relationship. As far as Lola is concerned, her mother's name is "Mami" and her grandmother's is "Abuelita." If you have to describe the relationship, it should be in English and should be an improper noun:
Lola's mother is Alicia, whom she calls Mami.
Lola's grandmother is Abuelita.
Please note that I do not speak Spanish and have a vague Latin background. I know Romance Languages have different suffixes that denote subject or predicate use of the word, so I don't know if "Abuelita/Abuela" is changed based on the character being the subject or predicate of a sentance. That said, since this is being used as a name in English (which doesn't change suffixes based on where a word appears in a sentance). It should be consistent.
It should also be pointed out that it's okay to give the actual legal names of the parents, but your MC as the view point character and your narrative voice, should refer to them by parent terms whenever possible. Your story should only use legal names if A.( It's in dialog and said by a person who would refer to these people by a legal name OR B.( It's a formal situation where the view point character has to identify them for a specific formal situation.
This includes the narrator who is effectively Lola's internal voice.
Some situations where you can drop the names:
"Alicia, you look divine," Lola heard Hector say as she went up the stairs.
"Carmen Ramone is my Abuelita... my grandmother...," Lola said to the police officer.
Edit: As a final note, as someone with no Spanish language skills at all, I was able to pick up on Abuelita being "grandmother" without the word being defined. Use context clues like having Abuelita tell Lola about when Mami was Lola's age how she would get into all kinds of trouble and how Abuelita would ground her so many times (or put in time out/ spank/ whatever discipline a parent would use on an unruly child).