A proposal will be presented for a new experiment, which has been developed with Los Alamos National Laboratory LDRD funding, to measure the neutron lifetime using ultracold neutrons in a magneto-gravitational trap. In the proposed experiment, an asymmetric bowl-shaped Halbach array of permanent magnets provides the levitating and laterally confining magnetic field for ultracold neutrons produced by the Los Alamos solid deuterium source. Quasi-trapped orbits, in which relatively fast neutrons may escape during the measurement period, are suppressed by the asymmetry of the bowl and small-scale field variations designed into the magnet array. Progress on the construction of the prototype apparatus will be described.