We study Lefschetz fixed point formulas for R-constructible sheaves with higher-dimensional fixed point sets. Under some assumptions, we prove that the local contributions from them are expressed by Euler integrals of some constructible functions associated to hyperbolic localizations. This gives an affirmative answer to a conjecture of Goresky-MacPherson for smooth fixed point components. In the course of the proof, some new Lagrangian cycles will be effectively used. More precisely, generalizing Kashiwara's characteristic cycles we introduce Lefschetz cycles and describe them explicitly by using hyperbolic localizations. This is a joint work with Yutaka Matsui and Kiyoshi Takeuchi.