Lightroom requires you to Import photos before you can do anything with them in Lightroom.
You can use the Add option when you import, which will import the photos but leave them in whatever location they are stored in.
For new photos, you can also instruct Lightroom to copy them from the camera card to your external HD.
Your photos can reside on any hard drive or even a network drive that is connected to your computer. The import process doesn't put the image "in" Lightroom, but rather simply creates a pointer in the database so that Lightroom can keep track the adjustments and changes that you make. Lightroom will create a preview image, and you can control the size of those previews making them smaller if space on your hard drive is limited. You can even move the folder containing your catalog to the external hard drive if you want. This would minimize the amount of space taken by the Lightroom program. The catalog can reside on any hard drive connected to your computer, but cannot be on a network drive.