Recently my MacBook (256GB) has been running very low on storage due to all the raw files I've uploaded to Lightroom. I just bought a LaCie external hard drive... If I copy all my photos onto it and then delete them on my computer's hard drive, can I still edit them in Lightroom?
Yes you can copy all your photos to your external drive. However, there are a couple of right ways to do it and some wrong ways.
If you do it from the operating system, LR will have no idea where they are. It is possible to use LR to find them again.
Another way is to move them to the external drive from withing LR. Then LR will know where they went and all edits will be preserved.
In addition to whsprague:
I'd move them with the OS and then relink in LR. Important: move the entire structure as it is and don't change the folder structure while copying. You then have to relink the top-most folder LR and all the sub-folders are corrected automagically.
ps: Do NOT try to re-import!