If you have the Lenovo set to output 60Hz and your TV is in 120Hz mode all it will do is show the same frame 2x every 1/60th of a second.
I don't believe the refresh rate settings in Windows can affect your TV like they would a monitor.
I could be wrong but that's my understanding anyway. For instance, ATSC TV is typically broadcast at 60Hz and your TV would be doubling that at 120Hz. If your source is 24Hz (say a blu-ray from a film) it would quintuple it (show the same frame 5x) to get to 120Hz.