Rapid advancement in the observation of cosmic strings has been made in recent years placing increasingly stringent constraints on their properties, with $G\mu\lesssim 10^{-11}$ from Pulsar Timing Array (PTA). Cosmic string loops with low string tension clump in the dark matter halo of the Galaxy due to slow loop decay and low gravitational radiation recoil, resulting in great enhancement to loop abundance in the Galaxy. The power of gravitational wave emission from loops is dominated by harmonic modes spanning a wide angular scale. Loops located in proximity to the solar system are powerful, persistent, highly monochromatic sources of gravitational waves with a harmonic signature not replicated by any other sources, making them prime targets for direct detection by the upcoming Laser Interferometer Space Antenna (LISA), whose frequency range is well-matched. At $G\mu=10^{-20}$, there can be more than $10^8$ loops contained in a narrow LISA frequency bin $\Delta f\sim 3\times 10^{-8}\ \mathrm{Hz}$, with an average separation of just a fraction of a kpc at solar system orbit. Unlike burst signal detection where detection rate simply scales with loop abundance, detection rate for harmonic signal is the result of a complex interplay between strength of gravitational wave emission by a loop, loop abundance, and other sources of noise, and is best investigated through numerical simulations. We develop a robust and flexible framework for simulating cosmic string loops in the Galaxy for the purpose of predicting direct detection of harmonic signal from resolved loops by LISA. Our simulations reveal that the most accessible region in the parameter space for direct detection consists of large loops $\alpha=0.1$ with low string tension $10^{-21}\lesssim G\mu\lesssim 10^{-19}$. Direct detection of field theory strings by LISA is unlikely, with the probability for detection $\lesssim 10\%$ under best circumstances, and $\lesssim 2\%$ with a more conventional configuration. Extension of our results predicts that direct detection by LISA of cosmic superstrings with low intercommutation probability is very promising, even unavoidable with optimal parameters. Searching for harmonic gravitational wave signal from resolved cosmic string loops in the Galaxy through LISA observation will place physical constraints on string theory.