Could you call The Sun Also Rises a satire?

I would not call it a satire because the formal definition of a satire is

"a literary work holding up human vices and follies to ridicule or scorn" (merriam-webster.com).

While Hemingway certainly sheds light on and discusses in detail the vices and follies of America's Lost Generation in the novel, he does not ridicule them or scorn them--most likely because he was a member of the Lost Generation himself. Instead of readers hating Brett and Jake, most feel sympathy for them and want them to be able to find happiness rather than jaded cynicism.  While it is, of course, impossible to know Hemingway's motives for creating such characters, it does not seem that he was trying to effect change by writing the novel--that is also the purpose of most satirical works (to encourage the subject of the satire to improve).  Rather, he seems to have written Sun to illustrate why members of his generation fled to Europe and engaged in frivolous lifestyles, perhaps hoping that his readers would better understand him and his peers.