I’d recommend getting started on contributing to ArviZ with a smaller issue to get familiar with the contributing process, PR, reviews and so on, and once you are familiar (one PR can already be enough, depends on the background of everybody) with that start working on LFO. In the meantime you can get familiar with the paper too and ask any questions about it here or in a new topic. I can also help in choosing a small feature that is related to your interests and the task at hand.
Regarding LFO, it should be added to stats_refitting.py like reloo, and the body of the lfo function should actually be quite similar and should use the same methods of the SamplingWrapper class as reloo. I will merge Refitting by OriolAbril · Pull Request #1373 · arviz-devs/arviz · GitHub in the near future so all the updates to the base sampling wrapper are available in ArviZ development version. When starting to work on lfo we can chat here or in gitter to discuss the api and how to modularize the code. And don’t hesitate to contact me at any point of the process.