I'm not a mind reader and I have not asked,* but I assumed from the get-go that what was driving the Miss Piggy comparisons was the hair. When I look at Miss Piggy, her hair is the very first thing that jumps out at me. That's true for me for L'Rell 2.0 but not in the same way.
Beyond their hair, I don't really see a parallel between L'Rell 2.0 and Miss Piggy. Even their hair doesn't quite click as a parallel, because Miss Piggy's hair is perfectly conceived to visually convey her character. On the other hand, L'Rell 2.0's hair seems way too human (i.e. out of place on an alien), especially the style, unless that turns out to be part of the point (cf B5's Delenn in hybrid form and her human hair).** However, the comment from somebody associated with the show about Klingons growing their hair out in peacetime doesn't imply that there's anything going on besides purely Klingon hair getting grown out and styled according to Klingon customs.
* - But maybe I should ask. ("Just ask!" /Leslie Jones) To people who see Miss Piggy in L'Rell 2.0, is it the hair or what?
** - Somewhat different considerations apply to talking pig Muppets than to makeup for sci-fi aliens, for me generally speaking, I suppose.