The layered honeycomb iridate α-Li2IrO3 displays an incommensurate magnetic structure with counter-rotating moments on nearest-neighbor sites, proposed to be stabilized by strongly frustrated anisotropic Kitaev interactions between spin-orbit entangled Ir4+ magnetic moments. Here we report powder inelastic neutron scattering measurements that observe sharply dispersive low-energy magnetic excitations centered at the magnetic ordering wave vector, attributed to Goldstone excitations of the incommensurate order, as well as an additional intense mode above a gap Δ≃2.3 meV. Zero-field muon-spin relaxation measurements show clear oscillations in the muon polarization below the Néel temperature TN≃15 K with a time-dependent profile consistent with bulk incommensurate long-range magnetism. Pulsed-field magnetization measurements observe that only about half the saturation magnetization value is reached at the maximum field of 64 T. A clear anomaly near 25 T indicates a transition to a phase with reduced susceptibility. The transition field has a Zeeman energy comparable to the zero-field gapped mode, suggesting gap suppression as a possible mechanism for the field-induced transition. © 2019 American Physical Society.