Adding / Updating custom lookups via REST API

Question :Need to be able to update or create new custom lookups via REST api.

**This post was created as part of a How to Service Request

(SR)Release: 23A

Summary of the question: We would like to update custom lookups via the REST API but can't find any documentation that describes how or if that can be done. For the most part we would like to change the display name for existing ones or add new ones via the REST API. 

The use case is a tool that synchronizes some data between sites such as Dev => Test. It works for regular objects just fine, but if new CODE values for the FCL's Lookup do not exist on the target (Dev) it can't create the object until it is created.