Will It Work

Solution
That's a Lenovo ThinkCentre M81? If so, power will be an issue. Lots of Lenovos use special connectors for power on their motherboards, which means you can't simply upgrade the power supply. So if you have a mini tower, and it uses standard connectors, then you can upgrade the power supply and get a 1060. The 'cable' you refer to is the 8 pin pci-ex cable the card needs right? That's why you need a new power supply.
That's a Lenovo ThinkCentre M81? If so, power will be an issue. Lots of Lenovos use special connectors for power on their motherboards, which means you can't simply upgrade the power supply. So if you have a mini tower, and it uses standard connectors, then you can upgrade the power supply and get a 1060. The 'cable' you refer to is the 8 pin pci-ex cable the card needs right? That's why you need a new power supply.
 
Solution