The Sarlacc, Space Slug and Hutt-Duneworm comparisons
In the Dune stories we have people living with a gigantic worm-like creature of sorts, which can’t stand too much water and is very long-lived. Not to mention, those ‘sand-worms’ are used to inspire the similar Sarlacc creatures in Star Wars, right down to life cycle (to some extent) and longevity. The biggest difference’s that the Dune sandworms can reach to heights of 450 metres but are suspect when it comes to the square cube law (as in something regulating size in the real world, especially in how big it can possibly get and how its body adapts).
The sarlacc sandworms have a height that’s much more plausible: they’re the same size as the blue whale. Let’s not also forget that Jabba the Hutt owned a sarlacc himself just as his would-be Dune counterpart Leto Atreides’s also linked to sandworms. Jabba’s own species is also similarly long-lived, just as Leto himself’s long-lived too. Not bad for a Dune character who inspired an entire species on Star Wars when you consider this. Though a better comparison can be made with the space slugs (which measure around 10 metres but can be 900 metres).
The revolt against machines
In the Dune stories, we have humanity revolting against machines (especially computers and robots). This is played out to some extent in Star Wars where there wasn’t just a war against robots but also some people discriminate robots themselves. There was even a bartender bigoted against robots. This is also played out straight in the Terminator movies when you think about it. (If one’s not mistaken, both Ridley Scott and HR Giger were tapped in to make a Dune movie with the Chilean Alejandro Jodoworksy but it didn’t go as expected as they went on to do Alien.)
Princess Leia–Princess Irulan and Ghanima
Luke’s sister as I think she may’ve partly inspired by Alia Atreides in terms of weapon proficiency. However in terms of her trajectory and own diplomatic training as well as strong-willed/forceful personality she’s more comparable to Princess Irulan. Just like Leia, Irulan also lived in constant fear of assassination and was also trained in combat (to some extent, given her link to the martial-artists/scientists Bene Gesserits). This would’ve been more evident in the earlier Star Wars draft as with the cloning thing. That and being kind of grouchy, though I think Irulan was kind of grouchy to Paul who was cheating on her.
The two similarities Leia shares with Ghanima’s that they’re somebody’s twin sisters and both of them get raised by somebody else after their mothers died. Ghanima got raised by Irulan and Leia got raised by another family.
Padme Amidala–Lady Jessica and Obi-Wan Kenobi
Both of them are mothers to the would-be twins and are equally strong-willed. In fact, if I’m not mistaken Lady Jessica was strong-willed enough to prefer to beget a boy, thus foiling her colleagues’ plans to some extent. Jessica also trained her son often just as Obi-Wan Kenobi’s a father figure to Luke Skywalker. Though I highly suspect that Jessica’s personality and role influenced the development of Padme Amidala and Obi-Wan Kenobi to varying degrees. Jessica’s a Bene Gesserit married to a nobleman, Padme Amidala’s a noblewoman married to a Jedi. Obi-Wan’s a Jedi as Jessica’s a Bene Gesserit.
Both of them are sort of martial-artists who’re proficiently trained to use supernatural powers well. Not to mention they’ve trained our dear heroes Paul and Luke in one way or another. (And to some extent, Leia and Irulan the former by her brother and the latter by the Bene Gesserits themselves.) I even suspected the force-ghosts (spirits of Jedis) are analogous to the other memory/genetic memory as presented in Dune or at least George Lucas’s interpretation of the same thing. This is both learnt by users if I’m not mistaken. The only real differences are that the Bene Gesserits are all-female so parsimoniously Rey and Leia could easily be members of that group and the Bene Gesserits are also marriage-brokers of sorts.