But is you did not get this android lollipop 5.1.1 official ota update then you can update your moto G 1st gen to lollipop 5.1.1 XT1033 manually by downloading the Official Stock ROM OTA update, thanks to XDA member for capturing this OTA update.
Follow below steps to update your moto G 1ste gen to latest android lollipop 5.1.1 manually.
gammerson.com is not responsible, if you damage or brick your device.
Do it at your own risk and follow the instructions properly.
#How to Update Moto g 1st gen to lollipop 5.1.1
2.Download official android lollipop 5.1.1 OTA update.zip for moto G from below link.
3.Now place the zip file in your internal/sdcard.
4.Open Settings->about->Check for updates.
5.You get notification of new update is available install the update.
6.Done!you have successfully update your moto g 1st gen to android lollipop 5.1.1.