Reddit mentions of Wolverine: Old Man Logan Vol. 3: The Last Ronin (Wolverine: Old Man Logan (2015))

That book will get you the complete run of the original Old Man Logan storyline. It introduced the character, and stands alone as it's own distinct story. It was originally written as a bit of an "Elseworld" story, and the events of the comics neither directly led to nor out of this book.

But...since then, Marvel has introduced the character into the mainstream continuity, including a mini-series during the Secret Wars event and an ongoing series since 2016. These books are great for those who find themselves fans of the Old Man Logan character, but IMO they are not to the same quality as the original story arch.

That may be more complicated of an explanation than you needed: the short answer is yes, that book will get you the full (original) Old Man Logan storyline.

A few other quick notes: The book is best (or, at least, better) if you have some general knowledge of the Marvel Universe (even just knowing the movies will enhance the experience) but the plot is entirely self-contained so anyone could pick up the book and have a full idea of what's going on. Subsequent Old Man Logan comics have been published, but they came a few years after the original storyline. They're good, particularly if you find yourself liking the character, but the original storyline is awesome.