You will need the logo to be in the correct file format first. That will ideally be as a PNG file, since the PNG format is better for the sorts of graphic shapes used in logo's compared to JPEG files, PNG also supports transparency which can be really useful. Unfortunately LR will not support using a .PSD or any other file type that supports vector graphics as a watermark. LR is also really poor at resizing the image used for the watermark, so ideally you will create copies of the logo file at the correct resolution to match the pixel resolution of your output. So if you are going to be producing image files at say 1280×853 pixels, then you want your logo file to be 1280×853 pixels too, while output at 5700×3800 pixels would require a matching sized logo file. Much better to create the logo at the different sizes yourself, where you have full control. Hopefully you will have the logo in a vector format, so that you can change the size at will, without affecting the quality of the image. Here a PSD file, that has not had the graphics elements rasterized or flattened will be fine, and the PSD format is compatible with being stored in LR, and can be exported from LR as a PNG for a full quality PNG file in whatever size will be necessary.
Once you have your graphic files sorted you just go the the Edit Watermarks dialogue, under the Edit menu item in LR, and in the top right corner of the dialogue window there are Radio button check marks for Text and Graphic formats, select Graphic and you will be able to select your graphics file for adding the watermark. You can just use one size of watermark file if you want, rather than keep changing the settings for different size output, but doing that at times the image will end up not looking so good when it gets resized, since there is no vector support.