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Lightroom cannot remove white space around a signature (maybe -- maybe -- Photoshop can)
ok thank you
If I understand correctly, you scanned your signature and now want the background transparent to put this as a watermark on your pictures?
This is possible with any decent image editor. If you have CC Photographers plan, you have the best tool to do this: Photoshop. If you do not have access to Photoshop, because you have LR 6, you may use Gimp or similar.
There are several ways to proceed. My favourite, if the scan is clean and high resolution: Channels to select...
<ctrl> click the Channel of your choice (I chose blue, but if your signature is in red, choose red).
The background (white) is now selected, and the foreground (black) not. Invert the selection (Shift-Ctrl-I or Select->Inverse).
Click the "mask" icon as shown.
The background gets transparent. You may save your file now as PNG. You can assign that PNG as your watermark. My guess is, that you want to refine this a little bit in Photoshop and keep a Photoshop original. JPEG files do not hold transparency, so they can not be used for this.
If you use Gimp or similar, the concept of selecting and masking is the same, but the way to get your PNG file is different.