You can retrieve this information by using the JIRA REST browser. Take a look at https://developer.atlassian.com/display/DOCS/Using+the+REST+API+Browser for more information. To get the data about Teams you can use http(s)://yourserver.yourdomain/jira/rest/tempo-teams/1/team?expand=true.
Hope this helps
Maybe I'm being obtuse (only been using Jira/Tempo for a few days); your solution gives me a list of dictionaries with all the team ids and names (so yay) but the leads and members are dictionaries with empty lists for the values of the users (although definitely populated on our site). I have expand set to true. I couldn't find anything relevant in the browser or docs you linked to.
This is not supported in our current Tempo Timesheets version. We value feedback and comments on how we can make Tempo better, so if you have a feature request, please create an issue in our Atlassian JIRA (https://tempoplugin.jira.com/browse/JTMPO).
Other users with similar requests can vote on these issues and contribute by adding comments that will help Tempo developers implement the request.
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