There are some suggestions below, however if you think you have a good idea we are completely open to suggestion.
We were originally thinking that a cursive font might look nice, but after a few mock-ups it didn't look that good. We're still open to that idea if you think you can do it nicely.
We really like the Kate Kanzier logo, as it has a regal touch, and has both a long and short version.
We also like standard block san-serif logos, like Chanel, Ted Baker or Manolo Blahnik.
We also like something pretty standard, but with a unique glyph or mark that makes it our own. If that is on the first letters of the words then we can use that as a shortened logo, like say Amazon.com with the 'a'.
One idea we thought might work is having the first letters of each word 'JL' as making up the logo, like Kate Kanzier, or the attached image.