Meant to say this earlier but my brain decided that it didn't need to show up for work today: I think LCP base is called "Like Cold Process" because it's supposed to have the look of cold-process soap and allow you to wrap the soap in paper. When I used the LCP base, though, I went ahead and wrapped it in plastic wrap anyway, so i don't know how the "low sweat" base does unwrapped firsthand.
group3studio, I don't know what to say about adding shea butter to LCP base, but hopefully someone else will! I've never tried that, so I don't know if it would cloud the base or reduce its lather. I know folks here do add butters and oils to their bases just fine, but I'm not sure what amounts would be best. Hopefully someone who has tried it can give you some advice.