99.9% of all mods runs on Forge. Now I am asking you honestly: Why would they?
Liteloader is better to use than Forge when it comes to client side mods. Them, like me, probably don't want to use the entirety of Forge to use this mod. Forge is bigger and slower than Liteloader. I'm not saying this mod should switch to liteloader, even if I would like that, just explaining why Liteloader can be more suitable than Forge, and that if you use Liteloader you might not want to use Forge because of this mod.
Using Liteloader when you already use Forge is not a big deal, but using Forge when you already run Liteloader you will probably have a game that uses more RAM and so on, but I might not be entirely correct.
For this mod to fully function, it has to be installed on the server as well. Otherwise you typically get a few (small) de-synch issues. That rules out Liteloader, which is client-only.
Also, because of Liteloader's poor performance in combination with Forge (or maybe it's because of Forge), making this mod Liteloader-only would make it virtually impossible to use this mod alongside semi-large modpacks. And since most of the people using mods play modpacks, that would drastically decrease the popularity of this mod.
And because Liteloader's codebase differs a lot from Forge's, it'd have almost no benefit to have both a Forge and a Liteloader version being developed by the same developer team.
Honestly, if you want something like InvTweaks for Liteloader, I think it'd be better of being a separate project. As in, a different developer team and a different mod written from scratch.
I was thinking about singleplayer, that's what I use it for, but you're right, it's a good point.
I don't know how much truth it is in that LiteLoader's performance would suffer because of Forge. I use them side by side with no issues, but I do not have a lot of mods or play on a server with those mods.
Please consider that it's not technically a "shield slot", but an offhand slot that happens to be able to hold a shield and has a shield icon. It can hold almost any item, though.
Also, the addition of the shield slot to Vanilla Minecraft by Mojang was done just as hacky as a typical mod would have done it.
So I'd understand it if the developers of InvTweaks can't or don't want to add auto-refill or auto-equip support for the shield.