This section is from the book "Anatomy Of The Arteries Of The Human Body", by John Hatch Power. Also available from Amazon: Anatomy of the Arteries of the Human Body, with the Descriptive Anatomy of the Heart.
The Lumbar Arteries are generally four in number on each side; sometimes, however, we meet five, and sometimes only three. They are larger than the intercostal, to which they are analogous. Each of them arises from the posterior and lateral part of the aorta, and passes outwards on the body of the corresponding vertebra, and then behind the sympathetic nerve and psoas muscle : those that are sufficiently high pass also behind the corresponding pillar of the diaphragm. The upper ones are also more nearly horizontal; while the lower descend with a gradually increasing obliquity. Opposite the corresponding transverse process, each of them divides into an anterior and posterior branch.
The anterior branch, smaller than the posterior, passes outwards between the psoas and quadratus lumborum muscles, and then between the quadratus and anterior layer of the transversalis tendon. The anterior branch of the first lumbar passes outwards beneath the last rib, and along the insertion of the diaphragm, and then on front of the quadratus lumborum: it communicates with the intercostal arteries. The anterior branch of the fourth, follows the attachment of the quadratus lumborum to the crest of the ileum, and communicates with the ilio-lumbar. All the anterior branches, moreover, communicate with the adjacent ones, and supply the quadratus lumborum and broad muscles of the abdomen.
The posterior branch of each lumbar artery first sends a small vessel through the corresponding lateral foramen into the spinal canal to be distributed in the spinal marrow and its tunics, and afterwards expends itself in the lumbar mass of muscles, and the integuments.