We discuss the nature of electron-lattice interaction in optimally doped Bi_{2}Sr_{2}CaCu_{2}O_{8+delta} samples, using the isotope effect (IE) in angle resolved photoemission spectroscopy (ARPES) data. The IE in the ARPES linewidth and the IE in the ARPES dispersion are both quite large, implying a strong electron-lattice correlation. The strength of the electron-lattice interaction is "intermediate," i.e., stronger than the Migdal-Eliashberg regime but weaker than the small polaron regime, requiring a more general picture of the ARPES kink than the commonly used Migdal-Eliashberg picture. The two IEs also imply a complex interaction, due to their strong momentum dependence and their differing sign behaviors. In sum, we propose an intermediate-strength coupling of electrons to localized lattice vibrations via charge density fluctuations.