Black and white images have been part of my photography for many years. I learned in the optical darkroom using b&w film and printing paper for that purpose and I was lucky to have two great tutors, one of them died a few years ago.
Today software makes possible what we could not even dream of when we were in the optical darkroom working with negatives.
I was taught about the importance of dodging and burning in, technics I still use with my conversions. In the "digital darkroom" we can do selective manipulations and that has contributed significantly to the improvement of our photography.
Your image is a very good one. I like to put some more contrast in my images and I understand that each one of us has his or her own taste. My definition of contrast easily could be totally different to what someone else calls contrast.
Modern conversion software are of excellent quality. I use Topaz B&W Effects II and I have enough parameters in the software to manipulate the image to my taste. Other conversion softwares are similar in quality. I am not familiar with Lightroom.
If indeed you are interested in converting images buy a book on b&w digital photography that will prove to be a great investment. The book could teach you more than we can here with our opinions.