One of the things I enjoyed about Joe Kelly and Mark Waid's runs on JLA was Kyle Rayner and Wally West's friendship. While most of the team got along well enough, they seemed to be simply coworkers, while those two became buddies. What's nice is that it didn't start out that way, and instead grew over time.
Though it's been months since I read it last, I was thinking about JLA: New World Order, Morrison's opening arc on the book, and Wally's attitude towards Kyle in that one. Wally clearly doesn't like Kyle. When they go to the Hyperclan base in Mongolia, he gives Kyle grief about making him wait - for a whole three minutes. The look Porter gives Wally as he checks his watch seems disgusted rather than gently mocking or anything friendly. I know Wally's often impatient, but I can imagine he'd have done the same it if was J'onn or Diana. When he saves Kyle from the one Hyperclan member who throws his shield at Kyle, Wally hands him some more guff about having to save Kyle twice*. When things turn in favor of the heroes, Wally disses him for beating one of the Hyperclan by dropping a giant green anvil on him. Throughout all this, Kyle's trying to give as good as he's getting verbally, but 'Yeah? Kiss my ring, buddy.' is kind of weak sauce**.
The one that sticks with me is Wally telling Superman he has some problems with this kid calling himself Green Lantern. I'm not sure whether he means he doesn't like someone using the name Green Lantern, or he just doesn't like how this particular person is acting. I could see it either way. Devon Sanders' "Kyle Rayner: Adult!" posts back on Seven Hells! demonstrated Kyle was a dope sometimes (even being chastised for irresponsibility by Impulse once). I could see Wally not approving of how Kyle handles things, thinking he's got no business wielding the most powerful weapon in the universe.
But I wonder if it's more about anyone calling themselves Green Lantern after Hal Jordan's "death". Barry Allen was Wally's uncle, and Hal was Barry's best friend, and if remember that one issue of that Flash/Green Lantern mini-series Mark Waid did, Hal was kind of the "cool uncle" for Wally. While there were other Green Lanterns, at least one of which (Guy) was on a team with Wally, they weren't exactly taking over for Hal, just serving with him. Kyle took on the title after Hal pretty badly tarnished his rep, and didn't seem as though he'd get the opportunity to repair it.
Still, I'd expect Wally to be more understanding of Kyle's situation than most of the League, since he's the only one inheriting his title from someone else***. Maybe that's what helped them become friends later, Wally realizing however much of a goofball Kyle might seem, he does feel the weight he carries with the name Green Lantern. It's not the same weight Wally felt when he became the Flash, with people (including Wally) wondering if he could live up to Barry's legacy, but it's heavy all the same. I find it funny it would take Wally awhile to recognize the similarities in their situations, considering how fast he can think.
* The first time I assume being when the speedster Zum charged at them and Wally lead him off, but it's not like Kyle was twiddling his thumbs during all that. He was fighting two members of the Hyperclan while Wally was off circling the globe.
** Which makes sense. Wally can run though dozens of possible insults in his mind in an instant, before selecting the best one. Kyle has to throw out whichever one insult he can come up with in the same span of time.
*** Diana might also qualify, but I'm not sure if, at the time of New World Order, it had been added to DC lore that Hippolyta was Wonder Woman during World War 2. If so, there are two circumstances I might considering mitigating. One, Hippolyta didn't give up the mantle because she died, and took it up again when needed. Secondly, it's Diana, she's an understanding sort, so she'd recognize Kyle's struggle regardless. Not because she sees a similarity they have, but because that's who she is. Heck, she told Kyle in the first issue he could call her Diana, and she barely knew him then, but he was on the team and she probably figured it was a way to make him feel like he belonged.