I know it's easier if you try to classify things in terms of what you already understand, but you really shouldn't try to shoehorn the political factions of other countries into Republicans vs Democrats. It's really just going to impair your ability to actually understand what's going on.
It's important to have some context though. Because it the Japanese libs are like the Australian libs then it is very different than e.g. the western European libs.
From what I can tell is that japanese baseline is quite conservative so all parties are quite different from what we would have under the same name in the west. Though, they are definitely not left like the name would imply.
For example, LDP is known for it's "Japan, Inc." policy which advocates for close ties between the government and business. LDP also supports for "traditional family values and social order" which in all fairness is a must for every major party in Japan.
In the west we'd probably refer them as centrists or slightly-right of center.
Komeito on the other hand is a much more intersting party which is a Buddhist pacifist party with conservative but socialist ideologies. TBH I fail to find a western equivelent reading through their wiki but as someone who spent some time in Japan as a foreigner their policy against kafka-esque beraucracy in Japan make me like them them at least a little bit.
Komeito on the surface look like Christian Democrats. Who would emphasise their welfare aspect more in Europe, too, if they weren't also the ones completely captured by business interest and they didn't have actual lefties to contend with.
...in fact, the LDP also looks like Christian Democrats, but nationalist wing. I suppose they do also have folks who are plenty religious but not enough for Komeito.
CDP looks interesting, their socdems and soclibs actually merged? Someone realised that petite bourgeois aren't the actual class enemy?
For example, LDP is known for it’s “Japan, Inc.” policy which advocates for close ties between the government and business. LDP also supports for “traditional family values and social order” which in all fairness is a must for every major party in Japan.
What's important to know is that the LDP has been in government since the 1950s in Japan. At this time Japan went through a huge economic transformation post-WW2, growing the economy massively. This success cemented the LDP as the party of economic success, even though Japan's GDP has shrunk since the 90s. This shrinking has happened during a time of population decline also, so GDP per capita has only stagnated until recently, making it easier to handle.
Through this time, desire for political change has been growing, but a 70 year incumbent is hard to shift. Sounds like they been given a black eye in this election, but still remain the largest party. The question now is whether they of the opposition are able to organise a ruling coalition.
In simplified terms, LDP is the center. Its policies span center-right and center-left. It's basically "the government" since WW2 and swings between left and right depending on the specific PM and their faction.