As I've mentioned before, I wanted to do a theory on Luck&Logic. But before that, I feel that I must gather some information and place it somewhere. So, I may as well place them here and have you look at it, just in case I missed something or got something wrong.
Here are the existing worlds, as we know them right now. Note that each of the worlds we know so far are named after numbers.
The Known Worlds of Luck&Logic
A world of "power" and inhabited by beast-folk. Battle is one of the key characteristics of this world, and most of its inhabitants are fighters or otherwise invaluable members in a fighting unit (such as Liliana). Initially, they entered Septpia because they wanted to seek out strong opponents for training purposes.
As a fun fact, you can read "Monolium" as "World of Oneness," which may contradict the aim of "being the strongest" of the invading Monolium foreigners, but also be an aesop about the power of Trance and how it was eventually used to fight (and presumably) win against them.
It's world icon (the thing on the bottom of every card) and insignia (the symbol you see on the effect box of a card, and on the booster box) has a prominent cross design. In some instances the earth as a planet is symbolized by a cross, most likely to show its lack of what we'd call modernization.
A world of "spirits" and inhabited by figures insipired by Eastern mythology and religion. According to lore, balance is kept there, between heaven, earth, and the underworld. They stepped in and helped Septpia fight the invading Monolium foreigners in the storyline that occured in BT01.
As evident in old comments by people of this wiki, it was referred to as "Jisphere" due to their world's spherical symbol. Also, if your wondering why the there are three magatama beads in a world that's based off the number two, well that represents the balance that Disfia is keeping between three aspects- heaven, earth and the underworld. The world's insignia also resembles the design on a bagua mirror, of which the bagua is a notable aspect of feng shui practice.
A world of "rationalism" and inhabited by robots and androids. Essentially, this is our stock "technology" world. This is considered a perfect world, because the desires of its inhabitants are easily granted, so they decided to invade Septpia to experience hardships. Guess a life where you get everything you wanted isn't all what's it cut out to be.
I suppose you can read "Tritomy" as "cutting in three sections," which makes no sense to me, so if you got an explanation let me know. Perhaps as a coincidence, this is the third foreigner-world that we are introduced into (Mono/Disfia came in at the same time, so...) that's introduced in the third regular booster set, and it is named after the number "three."
Both its icon and insignia are clearly inspired by technology, looking like circuitry.
A world of "myths," and home to what most people will probably know as the partners of the L&L heroes. While it says "myths" it actually covers only Western myths and religion (as evidenced by "Lucifer" and "Michael" of Christian beliefs, and "Quetzie" the Quetzalcoatl of Aztec origins).
Tetra-Heaven may be named as it is because its most prominent characters are gods (or from what we know, goddesses). The "Tetra-" is from the fact that it utilizes the level zone extensively, where you can only have four cards in (but thanks to "Angel's Gospel, Nina" that's now broken. If for some reason the plot of Hinalogi takes a turn for the serious, you can expect Nina to take a really big part in the fixing of the world.).
One thing I found weird is the clan's symbols. Its world icon is a sun, typically viewed as the "god" figure as it provides life, nurture, essentially what gods provide to humanity. It's world insignia looks like it's straight from alchemy, which most people will understandably associate with FMA, because...
After much digging (since I wasn't sure what to look for orz), the insignia resembles Metatron's Cube. a geometric figure involving thirteen equal circles with lines running across the center of each circle. The Metatron's Cube is also known as part of the sacred geometry, which is associated with the belief that a god is the geometer of the world. Sacred geometry is also used for magic/transmutation circles that has been with alchemy.
Predominantly, it features a Seal of Solomon with a symbol for the Sun in its center. Also note that there is what appears to be a second hexagram behind the first-noted one, giving us a pseudo-dodecagram, or 12- pointed star. The number 12 has a special meaning in some beliefs too- it is the number of completeness (12 principal Greek gods, Odin's 12 sons, Jesus's 12 disciples. There are a bunch of other symbolism I can find here, but I'll have to add that at a later date.....when I've deciphered them...
The world inhabited by humans. For all intents and purposes, it's a carbon copy of the real world, where the previously-mentioned creatures don't exist. What is noted in the world is that if creatures from the other worlds enter Septpia, they "adapt" to its "logic", and since its "logic" or "rules" dictate that those creatures don't exist, they become either human (almost all foreigners), animals (Daiga, a notable example), or something that resemble Septpian objects (like toys for some Tritomy members).
The name is supposed to be pronounced as "Septopia." The "-topia" suffix means "place." I couldn't find a value on "Seventh Place," but if you recall Lucifer's dream of "Sept-Heaven," that can be read as "Seventh Heaven," a synonym for being in great joy and satisfaction, and (according to some Islamic beliefs) is the outermost 'plane' or 'sphere' of heaven where angels dwell, or at the very least a place that mortals cannot comprehend. It kinda adds more to Lucifer's character now, doesn't it?
There's a lot of things you can find out if you dig in the lore of this game. There's a lot more things I wanna talk about. But as far as "scientific facts" go, this is what we have. This will be a backbone on mny theory, so feedback really is welcomed. Again, if there's anything I missed/got wrong, please let me know.