I see two options here. I tend to recommend the second option though since this is well documented. This does restrict you to using KV store collection though; CSV files are difficult to interact with via a REST API (I had to write my own in the Lookup Editor to make CSVs editable).
Here are the details:
Using the REST APIs in the Lookup Editor
The REST APIs for the Lookup Editor aren't well documented since I hadn't designed them for use outside of the app itself.