According to David Schuster Lollipop 5.1 to Moto G (2nd Gen) in China is fully deploy today.That means Moto G2nd gen in other location like US,UK,india and other country is going to get android lollipop 5.1 Update to there Moto G 2nd gen Soon.
For checking android Lollipop 5.1 Update in you Moto G 2nd gen Do the following steps.
#How to get Android lollipop 5.1 update in Moto G 2nd gen.
1.Keep the app called Motorola Update service Upto Date from playstore.
2.And you should be on stock android Rom android lollipop 5.0.1
3.Now Go to Settings > About device and Software update
4.If you get the update just follow the steps to install the update.