The Y560's Lenovo Energy Management program in Windows 7 allows users to select whether to charge to 100% to maximize battery RUN TIME, or charge to only 80% to maximize LIFETIME of the battery.
If set to 80%, the "80% available(plugged in,not charging)" message will be displayed. This can be changed back to 100% at any time.
In other words, choose LIFETIME if you would like to charge up to only 80%.
Choose RUNTIME if you would like to make it 100%.
These can be done in Lenovo Energy Management for your machine Z560.
The illustration below maybe a little bit different from other Lenovo Energy Management software but it should be around the same.