So I've thought about the Lip idea a little more, and whilst still a rough outline, I at least now have a better idea for how the combo/chain Puzzle Mechanic mechanic for Lip could work could work in SSB.
My problem with my initial idea is that it would have involved a good deal of micromanaging and encourage camping; that being to use Up B to set up a panel stack and then keep hitting it until you get combos/chains. My new idea doesn't entirely alleviate that possibility, but doesn't encourage it.
So rough Special outline would go as follows Neutral B = Quick Swap
Side B = Line Clear
Up B = Stack Rise
Down B = Garbage Block
In this move-set idea, both Lip's Up B and Side B (as well as potentially her Neutral B) would make panels with the chance for them being combo'd. The main way to not encourage spamming and/or camping is to simplify the combo build up by making it more auto (though not completely).
Stack Rise (Up B) would create a 3x6 row from underneath Lip, pushing her up with not only the initial rise, but also giving her an increased boost if any panels match and a line clear occurs. In this case, the chance of a panels forming a line of 3 or more is very likely. This gives Lip a combo/chain and a good boost, however, with each usage of her Up B within a certain amount of time decreases the likelihood of there being an automatically matching row of panels. Lip can adjust the panels through her B moves or by whacking the stack, but this leaves her exposed to attacks if she concentrates her time on building it up there and then rather than simply waiting.
In a similar fashion, the idea for Lip's Line Clear (Side B) would also cause a row of panels to rise out the ground; hurting foes who were atop that area. This would only be a row of 1x6 though, and in front of Lip. As before, the first time it is used, the chance of the panels matching is very high. Once matched, the panels disintegrate, damaging foes if they are still atop, and adding to Lip's combo/chain. As with Stack Rise, the chance for matching panels decreases with each usage. Having two moves that can create Panels, and thus build up the strength and size of her Garbage Blocks, allows for Lip to be more creative with her move-set.
I feel Quick Swap (Neutral B) could also have a panel creating aspect, working as a cursor which reverses the position of an attack or object with a panel. This only creates an additional panel, but can in turn be thrown about, and potentially lined or placed atop the Stack Rise or Line Clear to add to the combo/chain where otherwise there is not a matching Panel.
This panel matching mechanic would be for the purpose of building up Lip's two key assets; her Garbage Block and Lip's Stick. With increased combo/chain, the size and strength of her Garbage Block increases, her primary K.O, method. In addition, it adds to her Lip's Stick wielding smash attacks the flower affect; greater in respect to Lip's current chain/combo.
I ultimately don't see Lip as the best of fighters in terms of launching opponents, but I do see her as incredibly capable of blocking and building up damage; allowing her few stronger such as Garbage Block to launch her foes. An as mentioned before, I like the idea of having a divide between her Special Moves and A moves; Puzzle representation and flower representation. With Watabou, the floating flower from the menu screen and the rainbow bridges, Lip has plenty to draw from for aerial moves, whilst the Lip's Stick allows her to have a very unique smash style... thanks to smash.
This is only one idea, and did think of a couple others, but I felt they didn't quite fit. I thought about typing her combo/chain mechanic to her fighting style itself, how she can combo the foe with varied moves to build it up, but this led to a style of character that I didn't feel fit Lip nor a puzzle representative. Another idea is to drop the combo/chain mechanic altogether and focus on the 'damage building pro but weak launcher' design; it's simpler, but feels more like Lip as if she was made in/for SSB rather than as a representative of her gaming series.
I'll give more thought to making a better flowing move-set and how to iron the kinks, but what do you think of the rough idea?