Scientists use pairs of satellites to map the small variations in Earth's gravitational field. It is possible to see groundwater depletion and changes in distribution of glacial ice, among many things.

https://en.wikipedia.org/wiki/GRACE_and_GRACE-FO

The primary challenge in determining the mass of Earth is actually measuring the gravitational constant, G, itself. Everything else involved is known at much higher precision. The product of G and Earth's mass is known to two parts in a billion, but the uncertainty in G is ~22 parts per million.

https://en.wikipedia.org/wiki/Gravitational_constant

LISA is primarily sensitive to time-varying gravitational gradients on timescales of a fraction of a minute to a few hours and won't be terribly useful for determining the orbits of objects in our solar system. (but it is very, very cool).