Ultralight dark matter can interact with Standard Model particles via gravitational and non-gravitational interactions. Through such interactions, it can leave distinctive signals in gravitational-wave experiments. In this work, we investigate signals induced by ultralight dark matter quadratically coupled to the Standard Model in the future space-borne gravitational-wave detector, the Laser Interferometer Space Antenna (LISA). Due to the quadratic nature of the coupling, dark matter signals appear at two distinct frequencies: the frequency corresponding to twice the dark matter mass, and frequencies below the typical dark matter kinetic energy. We analyze both contributions and show that LISA can surpass current constraints from terrestrial and astrophysical probes in certain mass ranges. We also find that dark matter signals in LISA are free from screening effects which significantly limit the sensitivity of terrestrial experiments.