One of the signature goals of LISA is to test gravitation theory, and it seems unlikely that any other methods will achieve the sensitivity of LISA to deviations of strong-field gravity by 2028.
Unlike the ground-based instruments, LISA will have sufficient sensitivity to be able to notice small corrections to Einstein's gravity, and possibly to recognise unexpected signals that could indicate new phenomena.
By observing the long-duration waveforms from Extreme Mass Ratio Inspiral (EMRI) events, LISA will map with exquisite accuracy the geometry of supermassive black holes, and will detect or limit extra scalar gravity-type fields.
The MICROSCOPE (Micro-Satellite à traînée Compensée pour l’Observation du Principe d’Equivalence) mission will, by 2028, have improved our limits on the violation of the equivalence principle and could, of course, have measured a violation, which would make LISA’s strong-field observations even more urgently needed.
X-ray and other electromagnetic observatories may measure the spins of a number of black holes, but LISA’s ability to follow EMRI and merger signals through to the formation of the final horizon will not have been duplicated, nor will its ability to identify naked singularities or other exotic objects (such as boson stars or gravastars), if they exist.