Photoshop is an amazing program, but it's design has not substantially changed since version 2.5. Photoshop is a giant toolbox. It was designed for anyone working with photographs, including graphic designers, web designers, people doing magazine layouts, etc. Layers is perfect for magazine layouts, for example. Lightroom on the other hand was designed by the original inventors of Photoshop specifically for photographers. Lightroom is a workflow tool. It is ALWAYS nondestructive. Photoshop is only nondestructive if you use layers. Think of Lightroom as one giant super layer. Lightroom is faster than Photoshop, because you're working on a copy of the photograph, not the photograph itself. It is possible that if you're an expert at Photoshop that you don't need Lightroom. But even if you are a hard-core Photoshop-only person, you're probably also using Adobe Camera Raw and Bridge. Lightroom can replace Adobe Camera Raw and Bridge, and is much better at organizing your photographs.
Lightroom is also much more intuitive. If you want to lighten part of the photograph, you simply grab a brush and brush on where you want to lighten it. And once you have done this, you can move any of the other sliders to adjust contrast, white balance, saturation, etc. Making a mask in Photoshop and painting Black and white to adjust your selection is not intuitive. I watched Photoshop Week on Creative Live. Most of the Photoshop experts had as few as three or four and as many as 40 layers open so that they could go back and nondestructively redo any of the adjustments that they had made. With Lightroom you can go back to any of the adjustments you have made at anytime and tweak them. You can't do this easily in Photoshop unless you have created a layer for each adjustment. One thing I find frustrating with Adobe camera raw and Photoshop is after making my adjustments in Adobe camera raw and then opening the photo in Photoshop, after doing some work and then wanting to change an adjustment I made in Adobe camera raw it's not available. Yes, the newest CC does allow you some adjustments, or you can add an adjustment layer, but with Lightroom Adobe Camera Raw is always available.
Lightroom 5 also has an amazing Lens correction function. Yes, this did start in Photoshop, but Photoshop won't let you correct a photo with one click. Lightroom also has built-in tools for teeth whitening, Iris enhancements, and skin smoothing. Yes, you can whiten teeth in Photoshop, but it's much easier to grab a brush and do it in five seconds in Lightroom. With Photoshop, if you haven't made a layer for each and every adjustment, and you make too many corrections, you can't easily go back and correct something you did 30 moves ago. And the export functions in Lightroom are designed for photographers. I have one for Facebook with my logo, one without my logo with larger images for my website, and two or three others for printing photographs. And if you have a legal copy of the latest Photoshop CC, then you have a free copy of Lightroom. Why would you not take advantage of this?