I can confirm that it won't work. The 720/920 both require a minimum of 40w. I have a battery that outputs 20v/3.0A on USB-C and will not charge my Yoga 920.
I now use a Cygnett Chargeup Pro 20000, which outputs 45W on it's USB-C port, and it charges fine. Using a USB in line power meter, it tells me that the laptop is drawing 14.5v/2.8A (roughly, it fluctuates slightly of course) minimum to charge it viat the battery pack, which translates to roughly 40W
Here's the battery I use: https://www.amazon.com.au/Cygnett-ChargeUp-20000-USB-C-Power/dp/B0763H3GMV