dj_paige is correct. You really don't want to run anything without a backup. If you are going to run Lightroom with your image files stored on an external disk then you can just attach a second external drive and make a backup copy of your photos to it. This way, you can remove your image files from your internal disk and still have a primary and backup copy on two separate external drives.
Once you have the two copies on external drives, you can delete the contents of (1). You can delete the files in (2) as well but, being the previews that Lightroom generates, this will be only temporary. Each time you open an image in Lightroom, an attempt will be made to open the preview. If Lightroom can't find one, a new one will be created. Over time, you will be back to where you are now. Make sure you have your preferences set up to allow Lightroom to delete any preview that has not been referenced after thirty days (or even after seven) and this will help the previews.lrdata file smaller. Just make sure it is not set to never delete them. If you right-click on a folder in the Finder and select Get Info, you can see how much space the folder is taking up on the drive. You can also do this for a collection of files. Select the files you are deleting and then right-click on the selection.
You can also copy your Lightroom catalog to an external disk as well. This will cause the previews to also be stored externally. There is a drawback to this however. External drives are always going to be slower than an internal drive but, more than that, you can only work with your library when the external drive is connected to your Mac. If you are really desperate for HDD space on your internal drive, this may help but is not something I would do unless my situation were dire. Either way, if you want to store your image files on an external drive, you need to create a second copy of them or you risk losing them all. It is never a question of IF your drive will fail. It is just a question of WHEN it will fail. I keep three copies; my primary, my backup copy and an offsite copy and I update them regularly.