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Milky Way dwarf satellites are unique objects that encode the early structure formation and therefore represent a window into the high redshift Universe. So far, their study was conducted using electromagnetic waves only. The future Laser Interferometer Space Antenna (LISA) has the potential to reveal Milky Way satellites in gravitational waves emitted by double white dwarf (DWD) binaries. We investigate gravitational wave (GW) signals detectable by LISA as a possible tool for the identification and characterisation of the Milky Way satellites. We use the binary population synthesis technique to model the population of DWDs in dwarf satellites and we assess the impact on the number of LISA detections when making changes to the total stellar mass, distance, star formation history and metallicity of satellites. We calibrate predictions for the known Milky Way satellites on their observed properties. We find that DWDs emitting at frequencies $\gtrsim 3\,$mHz can be detected in Milky Way satellites at large galactocentric distances. The number of these high frequency DWDs per satellite primarily depends on its mass, distance, age and star formation history, and only mildly depends on the other assumptions regarding their evolution such as metallicity. We find that dwarf galaxies with $M_\star>10^6\,$M$_{\odot}$ can host detectable LISA sources with a number of detections that scales linearly with the satellite's mass. We forecast that out of the known satellites, Sagittarius, Fornax, Sculptor and the Magellanic Clouds can be detected with LISA. As an all-sky survey that does not suffer from contamination and dust extinction, LISA will provide observations of the Milky Way and dwarf satellites galaxies valuable for Galactic archaeology and near-field cosmology.