Very cute dress! Are the top & bottom two different fabrics? It almost appears that the top is a knitted fabric and the bottom a woven one. If the top is knitted and could be seen through (at the "holes"), then perhaps that's why it's lined, or if it's wool (so as not to scratch, but this doesn't look like a scratchy fabric). I think Joan may be right, that the skirt is supposed to be flirty and swingy, thus no lining to restrain it. Also, women wore slips back then most of the time, so even if the skirt part is semi-sheer, it would be fine unlined.
I agree with a 60's date, mostly because of the neckline. But the skirt certainly could have been 70s.