Certainly there is a tension between Lucy and Edmund in LWW, which isn't healed until he is rescued from the witch by some of the animals.  In PC there's tension between Lucy and Susan, when the latter isn't feeling brave enough to follow Aslan, but Edmund supports Lu.

I would say that in almost any story where the main characters are siblings, there are going to be tensions between them as well as friendships, as is normal in real life too. It'd probably be a pretty boring story if they all got along happily all the time, after all.

That said, though, I don't think sibling rivalry is an ultra-important theme in the Narnia books — it's there in some places, of course, and is an element of some of the plots, but they're not primarily stories about family relationships. We don't get to see much of how the Pevensies relate to each other when they're at home doing everyday things, or at their respective boarding schools, or what their relationships with their parents are like, simply because that's not what Lewis wanted the stories to focus on. And there are also tensions at times between the main characters who aren't siblings — Jill and Eustace, Shasta and Aravis, Digory and Polly — which are as much part of the plots of those books as tensions between siblings are in the books that feature them. So I can't see a good case for concluding that sibling rivalry, specifically, is a key element in the Narnia stories.

@coracle 

Right. Edmund teases Lucy about finding new countries in the cupboards in the house. Susan isn't brave enough to see Aslan, as Lucy is eager to do so.

@courtenay

That's true, it would be kind of boring if siblings or even the best of friends got along well all the time.

Then of course, there's Cor and Corin, who are twin brothers who have been separated. But there is nothing of a tension between them.

Then there's Letitia, Andrew, and Mabel. Letitia constantly tries to straighten Andrew out (it's likely she's the oldest of the three siblings).

Then Emeth and his six brothers (at least we assume he had six brothers, given that he's the seventh son). Yet, there is nothing of a tension with any of them.

@jasmine_tarkheena By your last comments we could  assume that everyone who's not an only child has rivalry!   Let's leave poor Emeth alone.

I think we can safely say that in most cases rivalry between siblings is a minor issue, and merely adds to their realism. Older brothers and sisters do look after younger ones. The next in line do challenge the oldest. The youngest may seem spoilt and the next youngest may be jealous. 

Edmund had something go wrong at school. This might be a good topic for us: what made a nice kid turn into what he in the first part of LWW ?

Right. Emeth should be left alone as it is.

I think in some cases, we could only speculate what kind of relationship siblings had. We could probably speculate what kind of relationship that Cor and Corin may have after HHB (I'm sure they got along fine, but that could be another discussion).

Even the ones that do have sibling like relationships (in the cases of Digory and Polly and Eustace and Jill), there is still tension. I think it's kind of nice to have two main characters that are like brother and sister, especially when they're not.

It could even be another topic on how siblings were able to show support to one another and what kind of role they may have portrayed (how Edmund was the only one to support Lucy when she's the only one who could see Aslan in PC or how Peter is protective of the other children).

IMO the sibling rivalry between the children is what makes the story so timeless and relatable for younger readers!

In my own writings on Narnia, I speculate that what makes the Jadis/Sister rivalry so compelling is the real-life story of Elizabeth I vs. Mary Queen of Scots.

@jasmine_tarkheena I think we can continue in that here - the contrasting behaviours. I love the way Edmund stands up for Lucy in PC. We can see his character is very much changed since his encounters with WW and Aslan.

Oh yes. And even in HHB, where Susan and Edmund are in Tashbaan, Edmund mentions that he would have loved her less if she had accepted Rabadash's marriage proposal.

While not a sibling rivalry, Corin is constantly getting into fights, yet is willing to let Cor (his long lost twin brother) to have the throne of Archenland.

@jasmine_tarkheena Corin doesn't get to make that decision: it's based on birth order.

@coracle 

True, he doesn't. The same could even be said about Caspian IX and Miraz. It was likely that Miraz was next in line after Caspian IX right up until Caspian X was born. That could have motivated Miraz to murder Caspian IX.

@jasmine_tarkheena Yes, that's what is understood, in PC & VDT.