After spending the week looking into more fashion designer branding research, I've started fresh with the logo design and come up with some new options.
Trying a different typeface for combining the L and M:
And another one:
Trying to change the shape slightly:
Lydia liked this idea but asked for more curves to be added in:
Adding in the lines from one of the other attempts:
Seeing how this works with her name:
Trying just the lines: