Thunderbolt™ Software installed itself on my laptop

Has anyone else experienced this program installing itself and is it safe?

This software was not installed by itself. It was included in a software package installed, you did install, which was either an Intel or Lenovo software package. This legitimate software can be safely removed if you are not using a Thunderbolt device.

Based on my research it was likely installed due to Thunderbolt™ Bus Driver for Intel or some equivalent previous version of the driver package.

I opened Lenovo "System Update" and checked for updates.

System Update is a Lenovo software package that will install software packages released by Lenovo for your device. System Update can be safely removed to prevent this from happening again. System Update does not install Windows Updates, it only keeps Lenovo software packages updated, which all can be downloaded manually.

Since it installed Thunderbolt Firmware Update Utility for T-Series which install the compatible version of the Intel Thunderbolt Bus Drivers for your device. The Intel link was only used to indicate that, the Thunderbolt Software application, is due to the drivers being installed.

Thunderbolt 3 Controller Firmware Update Tool for Intel is the Intel equivalent of this tool that was pushed to you. If you need the firmware tool, you should install the one provided by Lenovo, the Intel links are being used as an illustration that the software is legitimate.