You're world-building, so... yes?
For the first part, "Lich" is a label. It means what it means, and different worlds have different ideas of what exactly it is to be lich. If you're world-building, you get to answer those questions if you want. If you want a rogue or a warrior, or a paladin or a druid who is a lich, you can build a world where that fits and makes sense, and then put the appropriate character into it.
In general, "powerful spellcaster" is a big part of the core concept of a lich as a foe. They're a powerful spellcaster who's traded in their mortality and thus is also not particularly fragile, is hard to kill permanently, and has a vicious touch attack. So if you're imagining a lich who is not a spellcaster, then the real question is why? How is it useful that this character be a lich? Why do that rather than have them be a wight or a vampire or a necropolitan or a revenant or a deathknight or whatever? What does it even mean for them to be a lich, if they're not going to be a powerful spellcaster?
You're the DM, and you're trying to craft a game. That means that you'll have players, and they'll have expectations that you're working with, and those are going to matter. If you don't intend for them to find out that your ultimate antagonist is "a lich" then it almost doesn't matter what you call them. Just give them the features that you want and the backstory that fits it. If they are going to discover that they're facing "a lich" then they're going to have a set of expectations built around that, including things like a phylactery, undeadness, powerful spellcasting, and possibly soul-draining. If you're going to subvert one of those expectations in a big way, then you should have a reason for it - either because you actively want then to get the wrong idea just to mess with them (this sort of thing can work, but is really easy to do poorly) or because there's something particularly interesting and plot-relevant about "Why is this lich different from all other liches" that they can potentially investigate and get useful information out of. Even then, you'd have to have some reason why the information sources for the party concluded that this guy was a lich even without the spellcasting.
A "non-spellcasting lich" could be done, and it could be done well, but it should not be done casually. If your'e going to run with that, there should be some solid reasons behind it, and the fact that this particular foe does not cast spells in spite of being a lich should be a significant plot point that the PCs can discover, investigate, determine implications of, and gain advantage from. If you don't want "A non-spellcasting lich? How bizarre." to be a major plot point of your campaign, then you should either have your lich be a spellcaster (as normal) or you should call your non-spellcasting undead final antagonist something other than "lich". If what you really want is to have a non-spellcaster who has a phylactery (the only real defining point of a lich other than the spellcasting) then it might be worthwhile to toss something in there about how his apotheosis ritual was in some way derived from the standard lichdom rituals, but I still wouldn't call the result "a lich".