Can a plaintiff who failed to include a claim in their complaint amend the complaint?

"[P]laintiffs who failed to include a claim in their complaint can move to amend the complaint; if summary judgment has been granted to their opponents, they can raise the issue in a motion for reconsideration." Greenidge v. Allstate Ins. Co., 446 F.3d 356, 361 (2d Cir. 2006). Where, as here, the plaintiff chooses to pursue neither route, "a district court does not abuse its discretion when it fails to grant leave to amend a complaint without being asked to do so." Id.; see also Mauro v. S. New England Telecomms., Inc., 208 F.3d 384, 386 n.1 (2d Cir. 2000) (concluding that the district court did not err by refusing to consider a claim

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where the plaintiff failed to move for reconsideration after the district court's decision alerted him to pleading deficiencies).