Can you have lumbosacral neuritis without herniated disk?

yes: The neuritis just refers to irritation of the spinal nerves, which can be from herniated disk, bone spur, post operative scar tissue, doctor caused trauma from a needle, tumor, infection, metabolic/endorcine (ie diabetic poly-radiculopathy) etc... http://www.medicinenet.com/radiculopathy/article.htm.

A lot of terms: Neuritis/Radiculitis are synonyms suggesting sciatica pain but without significant exam findings. You can have tears in the disc causing chemical inflammation rather than mechanical irritation. Radiculopathy is a term for sciatica that causes, numbness, weakness and reflex changes on exam. Sciatica is term for all of the above but generally includes back and leg pain.