Yes, one would expect a suit from the 1940s to be lined, especially the skirt. The skirt looks to have been shortened? It hangs a bit oddly. The fabric looks like that rayon poly fabric that was popular in the 1970s, made to imitate the look of linen. It often would get little pills which I think I can see on the surface of the fabric? Hard to tell without an extreme close up.
Can you snip a tiny bit of fabric from the inner seam allowance and do a burn test?
Photos are often not the best clue, unless you can date them perfectly accurately and be 100% sure the garment is the same one in the photo. Original owner's memories can often be blurry after time. It happens a lot.