What do you like best?
What's not to like? Much easier for the amateur photo editor than Adobe Photoshop, this is a great program that many Photographers/editors of all skill levels can rave about. Top uses for this program: color adjustments, lighting/exposure adjustment, and the ability to print and export hi-resolution images which can be used for downloading, sharing, etc. Another great thing about it, if you need more advanced editing ...it can be integrated across other Adobe programs such as Photoshop.
What do you dislike?
The tool overlay function is a pet peeve for me. When using the spot removal tool (clone & heal), the tool overlay can be a little frustrating when you are trying to edit out a variety of spots, especially when whatever you are trying to edit is really close together.
Recommendations to others considering the product
You can't go wrong with this one, but if you need more advanced photo editing capabilities you will likely want other programs in the creative cloud suite as well.
What business problems are you solving with the product? What benefits have you realized?
Many business-related and creative tasks can be completed with Lightroom. It's great for small business application as well as large scale creative areas. As far as Photography, I've seen it used not just as a program for editing photos but also as a way to share presets (kind of like an editing template) among other Photographers/editors...which you can share for free or for a fee. It can also be used for slideshow presentations, print media (books, photos), and web-based applications.