How lineage helps to recompute data?
For example, I'm having several nodes computing data for 30 minutes each. If one fails after 15 minutes, can we recompute data processed in 15 minutes again using lineage without giving 15 minutes again?
Everything to understand about lineage is in the definition of RDD.
So let's review that :
RDDs are immutable distributed collection of elements of your data that can be stored in memory or disk across a cluster of machines. The data is partitioned across machines in your cluster that can be operated in parallel with a low-level API that offers transformations and actions. RDDs are fault tolerant as they track data lineage information to rebuild lost data automatically on failure
So there is mainly 2 things to understand:
Unfortunately, these topics are quite long to discuss in a single answer. I recommend you take some time reading them along with this following article about Data Lineage.
And now to answer your question and doubts:
If an executor fails computing your data, after 15 minutes, it will go back to your last checkpoint, whether it's from the source or cache in memory and/or on disk.
Thus, it will not save you those 15 minutes that you have mentioned!