Although Android 6.01 running on Moto G (3rd generation) is clean enough, the adult male component of sacchibelli’s family decided to hack his mobile phone to enjoy the new features of Android 7 (aka Nougat), in its stock version, without any addition or customization provided by Motorola or anyone else. This is now possible thanks to the team of Lineage OS, the former CyanogenMod custom rom providing the original flavor of Android OS. Here I listed the procedure I followed: it is a bit tricky and a bit risky too. A PC (in this case running Windows, but this is not mandatory) and a Moto G (3rd generation, 2015) updated to 6.01 is the needed hardware.

• To install adb and fastboot driver on (Windows, in this case) PC
• adb and fastboot are command line tools that allows to communicate with the mobile phone connected to the PC through USB
• Download the .exe from https://forum.xda-developers.com/showthread.php?t=2588979
• Install it on the Windows PC you are using to install Lineage OS on the smart phone
• To unlock the bootloader of the phone (aka, to root the phone)
• This is the step that makes your warranty void. A more detailed description can be found here
• Download the most updated USB drivers for Moto G 3rd gen from here, and install them on your PC
• On your Moto G, go to settings → About phone → build nuber
• Enable Developer options on your Moto G tapping build number 7 times until it says \u2018You are now a developer\u2019
• Enable USB debugging on your Moto G, going to Settings → Developer options → USB debugging
• Connect now the Moto G to your PC through USB cable; if any notifications about USB connection popups on your phone, please approve it
• Open a DOS command window on your Windows PC
• From here execute adb reboot bootloader to reboot your Moto G
• After the Moto G has rebooted to bootloader mode, please execute, always from the PC DOS command window, fastboot oem get_unlock_data
• A strange and long string like this one
  (bootloader) 0A40040192024205#4C4D3556313230
(bootloader) 30373731363031303332323239#BD00
(bootloader) 8A672BA4746C2CE02328A2AC0C39F95
(bootloader) 1A3E5#1F53280002000000000000000
(bootloader) 0000000
  will appear on your PC terminal
• Rearrange it in a text editor removing the (bootloader) text and writing all the numbers and letters in sequence, in this way 0A40040192024205#4C4D355631323030373731363031303332323239#BD008A672BA4746C2CE02328A2AC0C39F951A3E5#1F532800020000000000000000000000
• Go now to this Motorola bootloader unlock page where, after logging in with your Motorola account, you can check if your device can be unlocked
• Paste, in the appropriate field, the rearranged string you prepared in the text editor two steps ago and you will get an email with the bootloader unlock key written in upper case
• Type now the following command on your PC command window, to unlock your phone: fastboot oem unlock UNIQUE_KEY
• If no errors appears on your phone, your device is now unlocked
• To flash a TWRP Custom recovery
• This step, described in details here, allows you to install on your Moto G, the Team Wind TWRP Recovery, needed to flash then the Lineage OS custom ROM
• Download on your PC the latest TWRP Recovery for your Moto G (3rd gen) from here, and open a command window from the folder where this TWRP Recovery has been downloaded
• Type this command adb reboot bootloader to reboot your phone in bootloader mode
• Type then this command fastboot flash recovery twrp-osprey-3.0.2-r5.img to effectively install the TWRP Recovery on your phone
• Type then fastboot reboot to reboot your phone, once the TWRP recovery has been installed
• Create a Nandroid backup
• Before to go on, it is safer to create a Nandroid backup, using the installed TWRP Recovery
• The Nandroid backup procedure is well described at this link: http://droidvendor.com/how-to-backuprestore-data-via-nandroid-backup-using-twrp-custom-recovery/
• Eventually, install Lineage OS Custom Rom
• This is the final step, with the installation of Lineage OS custom Rom on your Moto G (see here for more details)
• Download, in your PC, Lineage OS 14.1 ROM for Moto G 2015 from here [Pick up the latest build]
• Download, in your PC, Lineage OS 14.1/Android 7.1.x Google Apps from here, choosing ARM as platform, 7.1 as android, and stock as variant
• Now transfer both files on your Moto G storage
• Turn off your device and reboot into TWRP recovery
• Select \u201cWipe\u201d from TWRP main menu and do a \u201cSwipe to Factory Reset\u201d on the bottom of screen
• Go back to TWRP main menu, tap on \u201cInstall\u201d and select the Lineage OS ROM .zip file that you transferred to your device two steps ago (lineage-14.1-20170207-nightly-osprey-signed.zip in my case)
• After selecting the .zip file, do \u201cSwipe to Confirm Flash\u201d on the bottom of screen to begin the custom ROM installation process. This may take some time.
• Once your ROM is successfully flashed, you\u2019ll see \u201cWipe cache/dalvik\u201d option, select it and then do \u201cSwipe to wipe\u201d on bottom of screen
• Repeat now the same step, from the TWRP main menu, installing the Google Apps .zip file (open_gapps-arm64-7.1-stock-20170208.zip in my case)
• Hit the \u201cBack\u201d button on-screen and then select \u201cReboot System\u201d button
• The Lineage OS boot logo should appear and you will enjoy the new Android 7.1.1 on your Moto G 3rd gen, although Motorola decided to stop the OS update to Android 6.0.1

Till now it seems that everything is working well, with the exception of the flash in the camera app. However other apps (like open camera) are able to drive the flash.

UPDATE: the following bug seems to be present (https://jira.lineageos.org/browse/BUGBASH-72?jql=text%20~%20%22osprey%22), with an issue in the transition from Wi-Fi to Cellular Data.