Hey guys! Guess what? I finally freaking figured out LZW Encoding. Here's a test result of a GIF I made. :3
Notice how there aren't two random color pixels at the end of the image anymore?
EDIT: Woo hoo! I got transparency working good too. :3 I haven't gotten it to work completely, you have to have a colored background on the images that you'd like to be transparent. (And if you're on a light theme, yes the first gif in this post does not have a transparent background)