No, not directly. Lookup FILES only work with CSV files.
You may be able to implement an external lookup with a script which parses your JSON data and returns matched values, but you would need to build this yourself.
Alternativly, you could write the JSON data into the KV store and use a KV lookup instead.
There are a couple of approaches for this, but if the json file is updated frequently, you may just be better finding a repeatable way to convert the json data to CSV.
@to4kawa read my mind 🙂
This would also work if you are already indexing the json file (or can).
You could even use this approach to populate a kv lookup using