The Life of a Machine is a timed Lightning Returns: Final Fantasy XIII side-quest available in the area known as the Dead Dunes.
Since it has a time limit, The Life of a Machine is a quest that can be failed; therefore, in order to complete it you have to move as fast as possible.
The Life of a Machine can be played after you finish the main quest named Where the Clavis Lies, as you enter the Temple Ruins.
Once you complete the said quest, you will have to return to the surface and retrieve 3 tablets that will allow you to examine the murals for main-quest 4-4: Murals of the Gods.
While searching for the tablets, it is a good idea to locate Bhakti’s Oil because you will need 3 units, and you should have them in your inventory before finding Bhakti.
This trick will help you finish the side-quest as soon as you activate it. Bhakti’s Oil can be found in various places, but there is one area in Dead Dunes where you will find all 3 units, and the following walkthrough provides all details on where to look for them.
Description: “In an Isolated chamber of the Sacred Grove in the Templar Ruins, Lightning finds an exploratory rover bot called Bhakti. It seems that he is almost out of fuel, but Lightning might be able to help.”
Location: Dead Dunes
Requirements: Finish main-quest 4-3: Where the Clavis Lies
Rewards: Maximum HP + 80, Strength + 4, Magic + 4, Cyber Scanners Adornment
While working to retrieve the tablets for the galleries you need to unlock in Murals of the Gods you will eventually have to explore the Dry Floodlands and Shrine of the Tablet: Dry Floodlands.
After you get the tablet inside the shrine, exit the structure and open your map.
North-east from the shrine is a dead end, close to Ruffian. Make sure you explore the location because there you will find Zanford (Last One Standing side-quest).
After you talk to him, look on the ground and you will see 3 glowing patches. Examine all of them and collect the three units of Bhakti’s Oil.
Now, return to temple ruins and check the Sacred Grove located west from Chamber of Floods (Sacred Gate). Look for Bhakti, the small red robot, and activate the quest, then give him the oil. Continue to watch the cutscene, and then enter the room nearby following Bhakti.
Right around the corner you should see several skeletons on the ground. Examine them to get the Pilgrim’s Crux, and then talk to Bhakti again to complete the quest.