Lightroom and Photoshop serve different purposes and complement each other.

LR is a high volume, batch processing, keywording/organizing/search, and light editing tool. It's useful for making proofs (print or digital), maintaining catalogs and websites, and making slide shows, among other things. The image editing/optimization in LR is mostly limited to global adjustments. I usually spend less than a minute on an image in LR. For more finely finished work, pass off images from LR to PS.

PS is the mac daddy of image processing and optimization softwares. You can work right down to the pixel level if needed and can use multiple layers, masks and other tools for extremely precise work. Way, way beyond what can be done in LR. But PS's weakness is it's rather slow and cannot efficiently handle large volumes of images, and doesn't have much in the way of cataloging/keywording/search tools built in. For those functions, you need LR.

Hence, the two complement each other nicely.

Some folks who don't do a high volume of images get by fine with PS alone. Other folks who don't make finished prints of high quality and don't have any other high use for their images... maybe only display and share stuff online, make small prints occasionally for scrapbooks, for example... might find LR alone is adequate for their purposes.

Adobe Elements is a bit of each... It has "lite" versions of some of the major features of PS, along with some other features drawn from LR... Some even find Elements adequate for all their purposes.