Observations of the rotation curves of large galaxies like the Milky Way have firmly established that there is a massive unseen halo influencing the dynamics of the luminous stellar population. Dark matter searches, coupled with computational models of galaxy assembly and growth, have attempted to constrain the nature of this dark halo, but gravitational lensing studies have failed to fully explain the mass observed. Across the gravitational wave spectrum, there are promising observations to be made that can probe the dark halo, particularly if the dark matter emits gravitational waves. In the vicinity of the Milky Way and the nearby universe, LISA will be the pre-eminent gravitational wave observatory for searching for stellar-mass gravitational wave sources. In the context of binary systems, LISA will be sensitive to ultra-compact binary systems with kilosecond astrophysical periods across the entire Milky Way, a scale commensurate with probing the spherical halo for stellar-mass binaries that can contribute to the dark matter halo profile. This paper considers the observable gravitational-wave signature of modeled white dwarf populations in the dark halo in the parameter space that is currently unconstrained by previous searches for clumpy halo dark matter. Population synthesis using COSMIC is utilized to consider a wide range of models to illustrate the constraining power of LISA observations.