Low back pain. 8 mos post laminectomy. Need good lower back strengthening exercises. Pain dr. Claims says its bio mech changes in facets post surgery?

Possibly. There is nothing about a laminectomy that should precipitate facet pain/arthritis. But patietns with spinal stenosis who require laminectomy often have multiple back issues including facet arthritis. There could be scarring after surgery causing some pain but typically you would have some leg pain as well. After completing pt and core exercises, facet pain can easily be tested with an injeciton.
Core. I would recommend formal physical therapy if not done recently. Granted it's time consuming but having someone observe your technique and plan for increasing your program intensity is valuable. Main home core programs should be discussed with your surgeon. They include front plank, side plank, (goal for >1minute planks) hamstring stretching. I would avoid sit ups, dead lifts, squats.
It could be facet. Pain, but often during laminectomies they obliterate the medial branch that feeds the facet, so it is not the only possibility and other things, like post-laminectomy syndrome, should be considered. A diagnostic block of the medial branch can be an easy way to find out if those small nerves are causing the pain or not. Pt should still be in the discussion as well.
Could be anything. Many things can cause pain after surgery. Scar tissue, re-herniation, facet disease, weak muscles etc... Recommend start with the basic stuff like working your core and pt and if that does not help consider repeat MRI first before attempting other options that pain doc suggests.