Can A Non-Exclusive Trademark Licensee Sue for Trademark Infringement?

No.

Hollywood Collectibles had a license to manufacture knives in connection with the trademark RAMBO.  (The knives were replicas of the knives in the first three Rambo movies.)  Hollywood Collectibles granted a sublicense to Master Cutlery.  After the fourth Rambo movie was released,  Hollywood again obtained a license to manufacture replica knives, and again granted a sublicense to Master.  Both sublicenses to to Master expired in 2010.  The parties attempted to negotiate another sublicense, but that did not work out.  Hollywood formally terminated the sublicense in 2012.

Master continues to manufacture replica knives, so Hollywood sued for (among other things) trademark infringement.  Master moved to dismiss for lack of jurisdiction, as Hollywood didn't have standing:

Lanham Act's cause of action for infringement of a registered trademark, 15 U.S.C. § 1114(1), is available only to a “registrant” of the trademark at issue, a term the Act defines as extending to the actual registrant's “legal representatives, predecessors, successors and assigns.” 15U.S.C. § 1127. Under some circumstances, an exclusive licensee has standing to pursue a trademark infringement action. See, e.g., Drew Estate Holding Co., LLCv. Fantasia Distribution, Inc., 875 F.Supp.2d 1360, 1366 (S.D.Fla.2012) (citing cases). However, in both of the licenses obtained by Hollywood Collectibles, the licensor retained the right to manufacture and sell Rambo knives for promotional and other purposes .  As a nonexclusive licensee, Hollywood Collectibles lacks standing to pursue a trademark infringement claim.

Motion to dismiss granted with prejudice.

Hollywood Collectibles Group, LLC v. Master Cutlery, Inc., Case No. 6:14-CV-176 (M.D. Fla. May 22, 2014) (J. Presnell)