To expand on Dan's post. When exporting images from LR they will always be RGB colour JPEGs that are exported. For monochrome images normally they will be R=G=B, but this can vary depending on the colourspace used, as some printer profiles will allow for the fact that you might have to shift the colours a little to actually achieve a neutral tone at any particular brightness level. You can see this in the LR Soft proofing system. If you select a printer profile it is likely that the histogram will start to show slight colour separations at the edges. If you pick a general space such as sRGB, aRGB or even ProPhotoRGB then the histogram stays as fully grey. In Photoshop (and other applications too) it is possible to convert the image to a true monochrome one, where there is only a single 8 bit data channel. You can tell that the image is true grayscale, as it will be only 1/3rd the size of the same image with full colour R=G=B channels.
Except for when having prints on Ilford black and white paper at Whitewall I now always use LR to export images in monochrome as full colour files. For prints this seems to give me quite reliable results with both my local Canon inkjet printer, printing direct from LR, and printing on Fuji paper at a lab. I do though use the labs pro service which makes zero changes to the image, and requires the image be exported using the labs own printer profile. Possibly the biggest problem with getting good monochrome prints using a colour printing system is consistency. It only needs a change in the batch of paper stock, or ink. Or in the case of wet lab prints, the chemistry to be a little off, miss mixed, or towards end of life and you can get some quite big changes in tone. For a consumer lab, a large number of clients, printing snaps are not going to notice a that there is a very slight colour cast in a colour image, our eyes are very used to adjusting that sort of thing out in the real world anyway. The issues come when you have a more discerning customer, and they are looking at a monochrome image, then it becomes very easy to notice a slight colour cast, and it can actually become quite a big issue.
Alan