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We merge the dispersive relation approach and the ab initio method to computenuclear structure corrections to the Lamb shift in muonic deuterium. Wecalculate the deuteron response functions and corresponding uncertainties up tonext-to-next-to-next-to-leading order in chiral effective field theory andcompare our results to selected electromagnetic data to test the validity ofthe theory. We then feed response functions calculated over a wide range ofkinematics to the dispersion-theory formalism and show that an improvedaccuracy is obtained compared to that with the use of available experimentaldata in the dispersive analysis. This opens up the possibility of applying thishybrid method to other light muonic atoms and supplementing experimental datawith ab initio theory for kinematics where data are scarce or difficult tomeasure with the goal of reducing uncertainties in estimates of nuclearstructure effects in atomic spectroscopy.

Dispersive evaluation of the Lamb shift in muonic deuterium from chiral effective field theory