There are a lot of different ways to convert a color image to Monochrome. One of the quickest ways is to use Lightroom’s Black & White converter either in the basic section or the HSL section. It does a pretty good job at converting to monochrome and it is fast and easy, I use this when I need a quick monochrome of an image, it does OK, but there are better ways and just about as quick. You need to use plug-ins made by Nik, Macphun, On1 or Topaz (I have tried but do not own), they all do a really good job, they give you presets to help you choose from to make the best monochrome images. They all work about the same, they let you make fine adjustments to contrast and the highlights and shadows. Plus you can make adjustments by changing colors as if you were changing filters on your lens, there are green, yellow, red, blue and grey, plus you can vary using in-between colors. This works well for bring out changes in different colors to the various shades of grey. I would use it to bring out the leaves to contrast with the sky, or brighten or darken the sky itself. All to get the contrast and shading of grey to make the best monochrome image.
I started with this original color image:
These are the different versions using the different plug-ins.
They all give acceptable results, but do achieve it in different ways, so experimenting with the different plug-ins to see which you like the best. I found I like both the On1 version and the Silver Efex versions the best, but they are all very close. If you need only one set of plug-ins, I would probably go with On1 or Nik. The only worry I have is that they have not been updating the Nik software, but On1 and the rest are constantly improving their versions. All of the plug-in do have trial that you can try before you buy, so try them and see which ones does the job for you.
Here are links to video tutorials for the different plug-in companies: