I actually feel Minuette’s the Pinkie Pie of the Unicorn 6 (though it’s possible Minuette’s the Twilight Sparkle of the Unicorn 6, as Twilight herself certainly wasn’t)  
I guess Minuette and Lyra took different ‘aspects’ of the two’s roles:
 
My ‘headcanon’ involves unofficial ‘lesser’ elements of harmony - nothing with ‘mechanical’ effect, but there’s three pairs who partially share elements.  
RD and AJ everyone’s commented on, if you watch reactions - there’s a bunch of times one of them’s been closer to the literal interpretation of the element than the actual Bearer, though I personally argue they do have the right ones.  
Rarity’s ‘Generosity’ and Fluttershy’s ‘Kindness’ are practically the same thing, especially the way they portray them, so it’s mostly about exactly how they’re generously kind - incidentally, while I keep in mind that Rarity was meant to be the Element of Inspiration, I actually prefer Generosity; Currently, the Mane 6 make up the ‘foundations’ of a Friendship, while Inspiration would have been the odd one out (Inspiration’s great and all, but it’s unrelated to friendship)  
But the relevant one here is Twilight and Pinkie, who both help keep the friendship together - Without Twilight, it’d be five ponies who live in the same town, and probably are friends with a couple others in the group, but are ultimately not connected. Without Pinkie intentionally being comic-relief and energetically extroverted, the life-or-death situations the six get into might have turned it from a friendship into more of a ‘sisters in arms’ thing.
 
Point is, if Twilight’s more introverted, but is the ‘cornerstone’ holding the others together, and Pinkie’s full of extroverted energy/excitement, then maybe Minuette’s the Extroverted Cornerstone and Lyra’s Introverted Energy/Excitement.  
The other four of the Mane 6 are actually not that vital; Their roles in the friendship could be changed, and while it’d change the friendship it’d not break it the way a lack of happiness and a binding force would.
 
But, Lyra’s without a doubt Ponyville’s bounciest pony.  
Pinkie ‘skips’ sometimes while she walks, but Lyra bounces just so she doesn’t have to stand still (or because she can’t stand still)
 
And I definitively would have loved to see Lyra’s role in the Unicorn 6, back in their school days - especially to see her do some magic.

@Phantom Rider  
So true.

@MezzoDragon  
I for one have always thought of her that way. Mostly due to the hopping around with the Pinkie-class :D that gave us the “irrational exuberance” tag in more than one scene. Though eclipsed by the humans thing and Lyrabon, it’s sorta her ‘thing.’ So if Lyra’s hopping up and down on a cloud, it’s not because of some complicated spell, it’s because she’s Lyra and sometimes you just gotta say “she’s Lyra, don’t think too hard about it.

Lyra was depicted as an alicorn once. Though, I want to believe Lyra is the unicorn version of Pinkie Pie. As in she has the ability to defy logic. Along with being extremely giddy and hyper.

Animators really like her.

Well she did attend Canterlot Magic Academy for Gifted Unicorns.

Who Knew Lyra Could Walk On Clouds As Much As Twilight Sparkle Did? :0

Go home, Lyra. You’re drunk.

Wait… Lyra you’re not a pegasus…