An LLC's citizenship is not necessarily the state where it's based or where it's formed. It's based on the citizenship of its members. Figuring out an LLC's members isn't always easy because it often isn't public information.  

FRCP 7.1 changed to require the citizenship of every party to be disclosed in a diversity case. This doesn't solve the problem of determining if a case is removable when filed in state court, but it will answer the question of whether complete diversity of citizenship exists pretty quickly after it's removed to federal court.  Thanks to my partner Andrew Harris for alerting me to this change in the Rules.   

(2) Parties or Intervenors in a Diversity Case. In an action in which jurisdiction is based on diversity under 28 U.S.C. § 1332(a), a party or intervenor must, unless the court orders otherwise, file a disclosure statement. The statement must name—and identify the citizenship of—every individual or entity whose citizenship is attributed to that party or intervenor: (A) when the action is filed in or removed to federal court, and (B) when any later event occurs that could affect the court’s jurisdiction under § 1332(a).