What I believe happened
I believe that Fine kept the fact that Izetta is alive from the whole world, and just let them believe that she had really passed on.
Only allowing those closest to her know the truth i.e: Lotte and Bianca.
Lotte decided to quit her job at the palace and had told everyone that she was going to move back with her sister. When in fact she was going to live with/ take care of Izetta.
Fine built a little cottage near the lake where they both had first meet, so that Izetta had a quite and peaceful place to stay. She would often visit Izetta as much as she could.
Bringing her gifts and the pie that they both love.
Fine would take Izetta outside and push her along the forest trails, talking, laughing and just having a great time with each other.
Fine would often tease Izetta by picking her up bridle style (que a blushing Izetta) grabbing onto the princess and burying her face under her neck.
Fine would alway carry Izetta to bed, help her get changed and tuck her in. She would also get in and cuddle with her and wait for Izetta to fall asleep, before getting up and kissing her on the cheek.
(The people at the palace would find it strange that their princess is gone every night. So fine can’t stay most nights, but she always visits the next day)
Also believe that Fine made a little garden for Izetta ❤️❤️❤️