Future searches for gravitational waves from space will be sensitive to double compact objects in our Milky Way. We present new simulations of the populations of double black holes (BHBHs), BH neutron stars (BHNSs), and double neutron stars (NSNSs) that will be detectable by the planned space-based gravitational-wave detector called Laser Interferometer Space Antenna (LISA). For our estimates, we use an empirically informed model of the metallicity-dependent star formation history of the Milky Way. We populate it using an extensive suite of binary population-synthesis predictions for varying assumptions relating to mass transfer, common-envelope, supernova kicks, remnant masses, and wind mass-loss physics. For a 4(10) yr LISA mission, we pr...