Start with Lone Wolf and Cub Omnibus Volume 1. There is nothing to argue about: this is one continuous story, serialised in Japan between 1970 and 1976, and Dark Horse's twelve-volume omnibus is the edition currently in print. Read the twelve in numerical order.
Say what it is first, because listings rarely do. Kazuo Koike wrote it and Goseki Kojima drew it, and most catalogue records including ours credit only Koike — the art is at least half of why the book is famous. Ogami Ittō is the shogun's official executioner, framed and ruined by the Yagyū clan, who takes to the road as an assassin for hire, pushing his infant son Daigorō ahead of him in a wooden cart. Each omnibus runs seven to eight hundred pages, and the pages read right to left, back cover first.
The gap in our list, stated plainly
We hold omnibus volumes 1, 2, 5, 6, 7, 8, 9, 10, 11 and 12. Volumes 3 and 4 are not in our catalogue. That is roughly 1,400 pages missing from the middle of a single continuous narrative, and it is our gap, not a gap in the series. Do not read Lone Wolf and Cub Omnibus Volume 2 and then Lone Wolf and Cub Omnibus Volume 5. Buy the two missing volumes separately — they are in print and easy to find — and slot them in where they belong.
What the early volumes are actually like
Mostly episodic. Ogami takes a contract, the contract is set out with obsessive procedural detail about Edo-period law, caste and weapon craft, someone dies, the cart moves on. The Yagyū revenge plot advances in short instalments for a long time before it takes over. Readers arriving from the film edits, or expecting a driving plot from page one, often find the first stretch repetitive.
That stretch is also where Kojima teaches you how to read him — long wordless sequences, weather, landscape, and the child's face doing work the dialogue never does. The last three volumes pay off in proportion to that patience, and they are the reason the book has the reputation it has.
The sequel
New Lone Wolf & Cub is a later continuation, written by Koike with art by Hideki Mori after Kojima's death in 2000. It picks up immediately from the end of the original, which means its first pages spoil the final volume completely. Read it only after volume 12. Most readers find it genuinely good and clearly lesser.
Do not mix editions
Three English collections exist and their numbering does not line up:
The First Comics run, 1987 to 1991 — flipped to read left to right, with Frank Miller and Bill Sienkiewicz covers, and it stopped a long way short of the ending.
Dark Horse's twenty-eight small paperbacks, 2000 to 2002 — complete, right to left, and still the numbering most online discussion uses.
Dark Horse's twelve omnibus volumes, 2013 to 2016 — the same material in the same order, larger, currently in print. This is what our list uses.
A recommendation to "start at volume 3" therefore means two entirely different chunks of story depending on which scheme the person meant. Pick one and stay in it.
Content
Extremely graphic violence, including violence against children. Several stories turn on rape and sexual coercion. Ogami operates by the code of his class rather than a modern one, and the book declines to editorialise about it.
Where it leads
Its influence is unusually traceable: Frank Miller's Ronin and Sin City, the comic and film Road to Perdition, which is openly modelled on it, and the six Baby Cart films made in Japan between 1972 and 1974 — the American recut Shogun Assassin is stitched from two of them and is not a substitute for reading it. The Lone Wolf and Cub hub has the rest of what we hold.
Follow the full ordered path here: Lone Wolf and Cub Reading Order: Where to Start Kazuo Koike's Samurai Epic.