The lacing on his back is probably just that. Lacing shows up on both solid and broken-coated (pinto) horses.
If you're planning on breeding these two, in addition to LWO I'd test for silver. Silver *hides* on chestnut so you wouldn't know just by looking. I've seen quite a few chestnut pinto appearing horses that were silver bay. Also, homozygous silver is now proven to be associated with Multiple Congenital Ocular Anomolies (MCOA). Here is a link to the UC-Davis color testing information:
The silver dilution dilutes black/brown pigment to lighten the manes and tails of black and bay horses to a flaxen or silver gray. The silver dilution is also associated with an inherited ocular syndrome known as Multiple Congenital Ocular Anomalies (MCOA).
vgl.ucdavis.edu
I know that I harp on this subject a LOT. I have a friend who bred Shetlands and focused on silver, so I saw it in many forms. I also saw the eye issues, before research had established the link between silver and MCOA. Save yourself the heartache and expense and please test. (For dwarfism as well, although I'll save that soapbox for another thread.)