Currently, the Jira Cloud Software REST API does not have endpoints for Swimlanes, neither for getting, adding or updating them.

It would be good to have this option as configuring and adding swimlanes to boards would be useful for automation.

As for workarounds, this is an unsupported one as it makes use of internal endpoints, and as such, they can change without notice:

We can have the Development tools open (usually F12 in your web browser), and then go to your board configuration, select the option Swimlanes, and then set them to "Queries" (since that is the only option that allows you to create custom swimlanes), and we will be able to see that a specific web request is sent like this one: 

Request URL: https://<Site name>.atlassian.net/rest/greenhopper/1.0/rapidviewconfig/swimlaneStrategy
Request Method: PUT

This has the body/date:

{"id":<Your board ID>,"swimlaneStrategyId":"custom"}

• In this context, "custom" is the internal name for the option "Queries".

Once this first request is sent, the Board configuration will be set to "queries" for swimlanes. 

Then, to add custom swimlanes when we add a new entry with a JQL with a request like this:

Request URL: https://<Site name>.atlassian.net/rest/greenhopper/1.0/swimlanes/<Board ID>
Request Method: POST

And in the body/data of that request, we add the swimlane data:

{"name":"<The name of the swimlane>","query":"<Your JQL query>"}

With this knowledge, you can set the board configuration to use swimlanes as well as create custom swimlanes through web requests.