It appears this is the way to get the rank information programatically now in new versions of JIRA. Take a look at the Communities post Changing rank through the API.
The Bob Swift CLI may be of assistance and you may be able to integrate that into what you're trying to do.
I think what you are looking for here is known as the JAVA API. This is not the same as the REST API, but it can provide you a programmatic framework to work with Jira.
You can find more on this at https://developer.atlassian.com/jiradev/jira-apis
You will note that there are published and updated JAVA API specs for Jira Core and Jira Service Desk. However at the moment, we do not appear to have an updated JAVA API document for the Jira Software versions, which stated with Jira 7. Jira Software is the component that handles aspects like lexoranking.
There is an open bug ticket to update this documentation at https://jira.atlassian.com/browse/JSWSERVER-15321
There are older Jira Agile JAVA API listed there, and those might be closely related to the current versions, but I cannot guarantee that the documentation for all aspects there are still applicable to the Jira Software versions.
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