My 2c:
Advantages:
* Image management & photo editing tools in a single product
* Images can be "tagged" and searched in several ways, including EXIF and IPTC metadata.
* Collections are useful to associate images from different folders without copying/moving them
* Editing tools are designed specifically for the photographer's needs, less to learn and master, simpler interface.
* Non destructive editing without any need to create separate layers. Virtual copies simplify different editing.
* Can apply the same changes to more than one image at once, presets help to speed up editing tasks.
* Very good support for cameras and lenses, custom profiles can be created when needed.
* Printing is designed with the photographer needs in mind (although it's not one of the more intuitive modules in LR...)
* Printing uses PixelGenius sharpening technology, available as a separate plug-in in PS.
* Not expensive
* Third party support, plug-ins are available i.e. from printers and calibration tools manufacturer.
Disadvantages:
* Not as powerful as PS for some more complex editing
* Not as versatile as PS, most editing techniques are "built-in", layers, masks, etc. can't be create manually and manipulated manually, and of course many of the tools available in PS are not available in LR
* Some other products may be better than LR at some processing tasks (although overall LR does an excellent job)
* LR uses only its own internal color space for editing. Different color spaces can be only selected for output (prints, exports).
* Little or no support for CMYK printing, separations, etc.
* Besides many RAW formats, LR supports only a limited number of other image file types.
* Images need to be imported into a catalog before being available for editing.
* GPU support has just been added to LR6, and still needs some polishing.
* The image management features are single-user only, doesn't scale to a multi-user environment (it's not a full Digital Asset Management solution).
Usually a workflow may be:
* Optional: pre-process RAW images in an external tool if needed, and export them in a LR supported format.
* Import images (RAW, or non RAW) into LR (applying presets if needed)
* Use its "Library" module to quickly tag, rate, reject, etc. images
* Use the "Library" module to select the images to work with, using its filter/search capabilities
* Use the "Develop" module to edit one ore more images
* If needed, export the an image to an external tool (PS, or others) for further processing
* Import the processed images in LR so they are available in the catalog for later searches, etc.
* If needed, soft-proofing and exporting/printing can be performed from LR, but also from other tools.
DXO Optics surely overlaps many of the LR features, and the only way to exchange images between the two AFAIK is using TIFFs or JPEGs losing the "non destructive editing" advantages (original images are still untouched, tough).
If your workflow already "works", probably you don't need LR. If you feel "something is missing", you should understand if LR could help you to fill those specific needs, or if you need another different tool. Sure, LR is widely adopted, but it doesn't mean everybody needs to use it.