Why can a new battery suddenly drop its charge?
There are three things at play :


IC in the battery that communicates battery parameters to the OS - not a culprit since you changed the battery recently
Hardware issue- unlikely, since you report it happening at random battery percentage values
Drivers in the OS, that read the values from the battery and amongst other things, display the battery percentage. This seems to be the culprit as you can see from the complaints in Lenovo forum. First post goes in length and after detailed investigation points the conclusion that the battery is fine but the problem lies with OS - system not showing the real amount of energy the battery still has, the reported values are much lower than actual leading to the device being shut down for prolonging battery life ( deep discharge is bad for Li Ion batteries)


This problem ideally should have been ruled out after firmware upgrade, but if the upgrade did not address the root cause ( as is evident from multiple complaints), firmware upgrade didn't help. 

I guess you can complain to the company and add your voice in the forum