LISA detector will observe gravitational waves (GW) signals in the millihertz frequency band. One of LISA targets for GW source is a binary system with extreme mass ratio known as EMRI. LISA will detect EMRI localized at low redshift (a few Gpc away from us), therefore the signal, traveling accross cosmological scales, can probe GW propagation in an effective field theory that describes modifications of gravity. In this talk, based on an ongoing collaboration with Stéphane Ilic and Ippocratis Saltas, I will first motivate the scientific aims of our project to use EMRI to test GW propagation. Then I will review a simple model for the generation of EMRI waveform and the EFT framework for testing GW propagation at cosmological scales. If time permits, I will discuss about our approach to estimate source and cosmological parameters.