I'm just getting back into photography after many, many years and have a new DSLR (Nikon D5500) that I'm learning to use (as a frame of reference, I was into photography as a teenager and had a K1000 that I loved, but that was a very long time ago). I love that I can bracket so easily but now I'm starting to dabble in Lightroom and I'm wondering if bracketing is necessary. I can change the exposure with very fine adjustments in Lightroom so does this render bracketing redundant?
It depends on the situation. It is true that if you use Lightroom or similar then you can pull details out of the shadows and balance the highlights easily, especially if you shoot RAW (which I recommend).
There are still limits to this though.. you can't ALWAYS have an exposure that allows the camera to capture the highest highlights and the lowest shadows, so that's when bracketing is the way to balance out such a shot.
Taking a photo of a room for example with light streaming in through the window. Bracketing is possibly the only way in to end up with a photo that shows the room in all it's detail with anything other than a big white rectangle of a window.