Is there time limit associated with your Lite plan ("free tier") for Db2 on Cloud?

No. The Db2 on Cloud Lite plan is a free tier of service that does not have a time limit attached to it. Clients can use it for as long as they require usage of the cloud database. Additional details on the Lite plan can be found in this FAQ on dw Answers. Clients who signup in North America should select the "US South" region for the Lite plan option. https://developer.ibm.com/answers/questions/436870/common-questions-about-the-db2-on-cloud-free-plan/