There are many amazing books appropriate for 4th-8th graders within the 700-950 Lexile range, to include Newbery winners and best sellers. Lexile only measures text complexity (sentence structure, words per sentence, etc.), not content. Consider that Grapes of Wrath and Charlotte's Web both have a Lexile of 680, which is a "3rd-5th grade" score. With this information, you can ask teachers to reconsider the 1000 point cut-off. I've had some success with that.
But sometimes it doesn't matter. Sometimes, you just have to find a book for class that is over 1000 Lexile. (And sometimes teachers don't have any choice, either.) I recently found a couple of wonderful resources that will hopefully make your life easier.
Here is an excellent collection of books from the Brownsburg Public Library that includes classics, YA, and adult fiction and fantasy. I started reading adult fantasy in 8th grade, and it can be quite age-appropriate. For a 7th or 8th grader, I'd definitely consider Hitchhiker's Guide to the Galaxy by Douglas Adams and maybe try out some of the older fantasy books by classic fantasy authors like Mercedes Lackey (Owl Flight), Anne McCaffery (Renegades of Pern), and Terry Brooks (Sword of Shannara.) The pacing may be slower, but if you like any of these, those authors have tons of other books for you to enjoy, set in the same world.
And the Elkhorn Library has this incredible list for 5th and up of books that are 1000 Lexile and up. It gives a tiny blurb about each one, too, as well as Reading Counts points. Some of these would be fine for fourth graders, as well. If you haven't read Hatchet by Gary Paulsen, this is your chance to enjoy a fantastic book that is over 1000 Lexile, along with his biography GUTS! Bad Beginnings by Lemony Snicket is good for those elementary kids being told to read 1000 Lexile, to include fourth graders.
You can also ask for help from your local school or public librarian to find suitable books. Librarians excel at helping readers find the perfect book--and created both of the linked lists from this post. WE LOVE YOU, LIBRARIANS!
Another excellent option for 3rd and 4th graders is The Higher Power of Lucky, by Susan Patron, which won the Newbery Award. It's not on these lists, presumably because it's not technically over 1000 on the Lexile site (it's listed at 950L), but it is also sometimes rated as 1010L, as evidenced by its Junior Library Guild page. Either way, it's a fabulous book if you can persuade your teacher to allow that apparent 50 point difference (mention that it was a Newbery Award winner.)
These two lists were more effective for me than searching on Lexile's site, but you can do that, too. Lexile's site is more useful if you have a title that you need to check for its level, rather than searching for a title, in my opinion.
Happy hunting for your next required reading, and best wishes!
To young readers, I hope I can offer a smidgen of help & encouragement as you traverse the waters of school, friendships, and life.