Supposedly, there is a “ThinkVantage recovery utility”, which can be accessed either through Windows, or by pressing F11 during boot.  Neither worked for me.  Also, the magic one-button you were looking for does not exist on Thinkpads, only on Idea series – as far as I can tell.

So, 3 easy steps then:

1) https://pcsupport.lenovo.com/us/en/lenovorecovery

               Enter serial number, follow prompts to get recovery files.

2) run USB recovery creator

https://s3-us-west-2.amazonaws.com/ddstools.gdi.lenovo/win8/USBRecoveryCreator.exe

point it to the files created in step 1, create recovery usb

3) Hit F12 while laptop booting to access boot menu.  Boot from USB created in step 2.  Follow prompts.

4) Optional – Install Lenovo Vantage, it will update all drivers.  It also does other stuff and annoys with notifications, and thus requires some configuration to minimize it’s footprint.

Other relevant info:

–more info about using USB recovery stick:

https://download.lenovo.com/km/media/attachment/win10%20rusb%20pub_en_english_sp40m55672.pdf

–during boot: ENTER –> BIOS.  Windows key on first page

—https://support.lenovo.com/us/en/solutions/ht103102

—https://support.lenovo.com/us/en/solutions/ht035659