Laurel Lime Ridge is one of those unrefined parks where the "trails" are more like ATV paths or old roads, the markings look rather ad-hoc, and there are apparently no maps. 
In spite of that, or maybe because of that, it's a neat park, and if you can find your way to the look out, you are rewarded with a view up the Housatonic River. The overlook here is directly opposite the river from Birchbank Mountain in Shelton. 
Ice crystal formations in the paths were difficult to walk on in places. But pretty.
Along the top of the ridge there are a series of interesting rock formations, overhangs, and quarries. In the picture above you can see a thick gleaming-white seam of calcareous rock, which is unusual around these parts. This is rock with lots of calcite, as in calcium carbonate or lime. A ridge of lime. And a few mountain laurels. Which is presumably why they call it Laurel Lime Ridge.
Not sure what they mined it for. But this is the same rock formation that was mined for tungsten, silver, and other metals that pops up in Trumbull, Monroe, and Shelton (see geology map - the formation is in orange). So it was probably some type of metal. The stone ruins in the photo above were near a small quarry and were probably related to the operations there.
The park is about 210 acres, and as far as I can tell it is owned by the Seymour Land Trust. If you're interested in exploring, we parked at the end of the cul-de-sac for Tibbets Road. And I was happy to have my gps with us (found a geocache while we were at it). The trails are all very wide and eroded, and it looks like there may be a lot of ATV traffic in there at times, but we were alone during our visit.