Think about it this way, take a theory where the neutrino’s mass is ε for arbitrary small ε and take the limit as ε approaches 0.
Then all other things being equal the length the neutrino needs to travel in order to oscillate to a different flavor approaches infinity.
(More accurately, oscillation lengths are inversely proportional to the differences between squared masses of neutrino mass eigenstates. So you can’t set a lower bound to the mass of the lightest eigenstate, but you can set a lower bound to the masses of the two other eigenstates. (Each of the three neutrino flavors is a different superposition of the three neutrino mass eigenstates.)
Then all other things being equal the length the neutrino needs to travel in order to oscillate to a different flavor approaches infinity.
(More accurately, oscillation lengths are inversely proportional to the differences between squared masses of neutrino mass eigenstates. So you can’t set a lower bound to the mass of the lightest eigenstate, but you can set a lower bound to the masses of the two other eigenstates. (Each of the three neutrino flavors is a different superposition of the three neutrino mass eigenstates.)