How to definite the total life cycle of battery under a depth-of-discharge(DoD)?
The 'Life Time' of a battery is how you choose to define it. Often the manufacturer will have their own definition, and most folks go along with that, especially if the manufacturer is rating the things that are particularly important to their application.
There are several different aspects to the performance of a rechargable battery, all of which degrade as the battery is cycled.

How much charge can be stored, the battery capacity
How long it holds the charge, the retention time
Its efficiency from charge in to charge out (important for PowerWall)
Its internal resistance
Its power output (important for EVs)

The most common one used to define lifetime is the capacity. End of life might be defined as 30% of original, or 50% of original. That might be the most important thing to you, or maybe charge retention is, or internal resistance. If you're a big buyer or a government or military, then you would be able to ask the manufacturer to specify and test the battery to your definition. If not, you'll have to do your own tests.
When you go to buy a battery, read the datasheet carefully. Reputable manufacturers will state their definition for the 'end of life' of the battery.
There is an SAE standard for electric vehicle battery lifetime testing, but I've not found a non-paywalled version.