No worries. If everything works fine with the other laptop then it must be one of the above with your new Lenovo. If you have tried lowering the resolution on the Lenovo, cycling through the output sources with Fn+F7 to no avail I'm out of ideas. Do you have any other external display or monitors you can try with the Lenovo?
I have also checked the Lenox manual and found the following section, though it just suggest similar stuff to the above.
Problem: The external monitor is blank.
Solution: To bring up the image, press Fn+F7 and select the desired monitor. If the problem persists, do the following:
1. Connect the external monitor to another computer to make sure it works.
2. Reconnect the external monitor to your computer.
3. Refer to the manual shipped with the external monitor to check the resolutions and refresh rates that are supported.
– If the external monitor supports the same resolution as the computer display or a higher resolution, view output on the external monitor or on both the external monitor and the computer display.
– If the external monitor supports a lower resolution than the computer display, view output on the external monitor only. (If you view output on the both the computer display and the external monitor, the external monitor screen will be blank or distorted.)