Lightroom benefits from DNG in two main ways.
1: is that if you sync your metadata to the DNG files you basically have a portable Library - in that all Library settings are saved inside the files themselves. This allows you to hand off a file to the next person in your chain and all changes you have made are instantly there for them, no complicated (near impossible) syncing of libraries. You can do this with the XMP (XML) sidecar files for .nef / .cr2 / etc files, but this involves sending two files, and you have no assurance that the end user actually sees your file as you intend - you must assume they use the XMP file correctly - which is really point two
2: DNG can ensure fixed rendering. No other raw file gives you the assurance that changes you make at the best time (while the data is still represented as seen on the sensor, not as combined RGB pixels) are rendered properly for the next person.
3: DNG uses better compression than Nikon has added to NEF to date. Smaller lossless files.
As for what software reaps these benefits - I am an Adobe addict on my main Windows machine, and all the current Adobe products see what I have described above and more. My laptop runs Linux and all the tools I use there (dcraw-based tools such as UFRaw and Raw Studio) love DNG and suffer from Nikon's bloody encryption of the whitebalance metadata on current NEF. DNG allows me to take a file I've worked on in Lightroom at home and continue to work on it while on the road with my OSS tools.