We analyze the expected arrival time spectrum of supernova neutrinos using simulated luminosity and compute the expected number of events in future detectors such as the DUNE Far Detector and Hyper-Kamiokande. We develop a general method using minimum square statistics that can compute the sensitivity to any variable affecting neutrino time of flight. We apply this method in two different situations: First, we compare the time spectrum changes due to different neutrino mass values to put limits on electron (anti)neutrino effective mass. Second, we constrain Lorentz invariance violation through the mass scale, Msub.QG, at which it would occur. We consider two main neutrino detection techniques: 1. DUNE-like liquid argon TPC, for which the main detection channel is νsub.e+sup.40Ar→esup.−+sup.40Ksup.∗, related to the supernova neutronization burst; and 2. HyperK-like water Cherenkov detector, for which ν¯sub.e+p→esup.++n is the main detection channel. We consider a fixed supernova distance of 10 kpc and two different masses of the progenitor star: (i) 15 Msub.⊙ with neutrino emission time up to 0.3 s and (ii) 11.2 Msub.⊙ with neutrino emission time up to 10 s. The best mass limits at 3σ are for O(1) eV. For νsub.e, the best limit comes from a DUNE-like detector if the mass ordering happens to be inverted. For ν¯sub.e, the best limit comes from a HyperK-like detector. The best limit for the Lorentz invariance violation mass scale at the 3σ level considering a superluminal or subluminal effect is Msub.QG≳10sup.13 GeV (Msub.QG≳5×10sup.5 GeV) for linear (quadratic) energy dependence.