The X-Men's own Kitty Pryde is actually a Green Lantern in one dimension of the Multiverse. Marvel and DC may be competitors, but any bitterness in the rivalry between them is purely in the minds of their fans. The reality is that writers and artists work for both companies far too often for any real antagonism to build up, and both publishers are well aware that the old saying is true; a rising tide raises all boats. The health of the comic book industry as a whole depends on both companies doing well.
As a result, it's not uncommon for writers and artists to subtly reference the different universes. Where older comics simply hinted at their being part of the same world, the modern approach is rather more Multiversal in nature. Take Infinity Countdown Prime #1 by Gerry Duggan and Mike Deodato, Jr., for example, which suggested DC's Captain Marvel is an alternate reality Carol Danvers; or Action Comics #998, in which Booster Gold insisted he couldn't call his AI servant "Jarvis," because that's a "whole other timeline." It's all good fun.
One of the more amusing, and easy to miss, references is in Chris Claremont and Roberto Castro's New Exiles #5. The multiverse-saving team the Exiles are a group of Multiversal superheroes who have been plucked from different dimensions and have been charged with protecting the fabric of the Multiverse itself. They are most commonly associated with the X-Men, and several mutants from the main timeline have been part of their team on occasion. New Exiles #5 includes a version of Kitty Pryde, and something goes wrong with her experience of the Multiverse; she begins to "cascade" through different iterations of herself from other realities. On close inspection, one appears to be a Green Lantern.
All versions of Kitty Pryde tend to correspond with the one requirement to become a Green Lantern; they have never been willing to let fear hold them back, and indeed have proved they will even sacrifice themselves if necessary. The main version of Kitty used her powers to phase a giant bullet headed straight at the Earth, even though doing so bound her to it and may well have been fatal. The one seen in New Exiles ultimately gives her life to save the Multiverse.
As noted, this kind of subtle tie-in is hardly unusual. It's difficult to say whether this was Claremont's idea or Castro's; the Green Lantern doesn't reappear, so this is basically just a cool Easter egg. Still fans can't help but wonder what an alternate universe where Kitty Pride takes the Green Lantern's Oath would look like.