There isn't much to comment on this letter. Seneca receives a book by Lucilius and he enjoys it so much, he reads it from start to finish.
However, I'll take time to make some observations about this letter.
First - there is an in-depth, on-going conversation between Lucilius and Seneca, in the form of these letters. This is a Stoic practice - that of discussion, learning, asking.
Second - in addition to the letter writing, there appears to be more formal writing in the form of a book, to which Seneca is referring. This is also a Stoic practice - writing. We see this in Marcus Aurelius' Meditations as well as this book that Lucilius wrote. Seneca also was a prolific writer.
Why writing? Good writing involves thinking. It helps you organize your thoughts, put them on paper, and spell them out. But after that, you are not done. You must read it, check assumptions and logic. Is it accurate? Truthful? Honest? If not, then it's back to revising. The entire process helps your inner dialogue and self-critical analysis.
From the letter, note this tid-bit from Seneca:
Your subject also contributed something; for this reason you should choose productive topics, which will lay hold of the mind and arouse it.
The topic of writing is for the mind, which then leads to lived actions, which then leads to introspection and analysis which should lead to further education and correction which should lead to improved action and behavior. This is how writing can be productive and "arouse" the mind.