Palutena's gameplan is simple:
Jab -> grab -> d-throw -> read DI -> followup.
Throw in a few extra pokes (dash attack, f-air and b-air) and decent ground mobility, and hey presto, it's Palutena! To be fair, it's not a bad gameplan. It isn't great, but it's serviceable, and it works. Yet I can't in all good faith say it's sustainable in high and top-level play.
She is consistent, that much is certain. None of her moves are dysfunctional or broken in the traditional sense; everything does what it's supposed to do (even if some of their effects are fundamentally mediocre), and you can get by without using any of her specials if you're savvy.* She doesn't have wonky hitboxes or moves that just don't work the way they're designed to. If her moves were faster or hit harder or had better combo potential, she'd probably be a great character. But most of her kit is either too slow, too weak or doesn't combo well, so while her moves do what they're intended to do, they're just not very good. She doesn't even have the cheese factor to tip her over the edge into viability.
Still, she has a gameplan, and it's not that difficult to pull off. A good Palutena will play ultra-defensively and poke you to death if she gets half a chance. The core of her gameplay is fishing for the grab, however she can, and following you up until you hit the blastzone. Palutena's viability is totally dependent on how well she can play the defensive game, stay safe, poke back and get the grab followups. Faster characters that don't stand still and give her a chance to hit them, aggressive characters that shut down her defenses, zoner characters that can pressure her right back and characters that just can escape her d-throw shenanigans with ease - these are the characters that Palutena hates. Unfortunately, this happens to make up most of the best characters in the roster. Palutena doesn't have much options when she's faced with a character that doesn't respect what she can do and can beat out her very narrow spread of viable options.
Lightweight does nothing to mitigate some of her biggest weaknesses: her smashes still need the hardest of reads to be in any way practical, her tilts still don't have the frame data or range to be safe, she still has to fish for the grab and she still has to contend with the cooldown phase that just scuppers whatever options she has in the neutral game. What it does do is make her advantage dramatically better and, to some extent, give her better footsies options. She doesn't really need extra mobility or recovery potential, she's pretty well off in that sense, but it's a happy side-effect and not something I will stick my nose up at if it's offered to me. What she benefits from is the ability to chase opponents for more dynamic and efficient grab followups, and in some weird and wonderful cases, get the tasty 40% kill off the upper blastzone. Getting the grab is a tiny bit easier, in that she's faster and can better pressure and chase the opponent in footsies to get into a good position for the grab confirm, or she can just keep out of the way of whatever the opponent wants to throw at her in footsies. It makes her better at what she does best, and that's pretty great: she goes from a character with a weak neutral game and mediocre advantage to a character with a mediocre neutral and good advantage.
Yet it's still not enough to make her viable. She will still have her incredibly so-so specials that only function well in certain very specific matchups; she will still struggle in neutral to get the grab; she will still have difficulty resetting to neutral; she will still want for the abundance of quick, safe options that the best characters have. Her other customs, in tandem with Lightweight, make this magnificent fantasy something of a fun reality: Explosive Flame is a better and safer projectile than Autoreticle in just about every way, Super Speed scoffs at the very concept of footsies and opens up her pressure game and options for grab confirms and Jump Glide opens up even more options in neutral thanks to Peach-esque aerial approaches and its speed and versatility in its movement options helps her get out of disadvantage and edeguard difficulties that she'd otherwise struggle with. Custom Palutena is, in my humble opinion, pretty good. Other characters would be overjoyed to have the kind of custom options she does.
Even so, you can't just cherry-pick one and say that it will fix her. It won't. Her gameplan does stuff and it does it well, but it doesn't do it well enough to threaten the stronger, faster, safer, trickier characters. You can make it better and that will, by extension, make her a better character, but it won't fix what makes her fundamentally weak. Changing her entire special set might do that, or even just make her so good at what she does that her weaknesses don't matter that much, but one custom will not make her an ultra-viable threat. It will make her better, but I don't think better is enough. She needs more than that, and for better or worse, we just have to make do with what we have and hope we can make it good enough.
* If anything, her specials just embellish what she has in very niche contexts: Autoreticle is a good mid-range poke to challenge fatties, Reflect is good for projectile-heavy matchups, Warp can ledge-cancel in stages with platforms and Counter is, well, a counter, but it's theoretically better than having an empty space for her down-b. I won't for an iota of a second say that they're universally good specials, because they're not. But they do have their uses, however context-sensitive they may be.
MysteriousSilver
. You can punish a lot of well-spaced moves or any landing because you're invincible. 
