Aims. We studied the diffuse X-ray emission around the HII region LHA 120-N11, which is one of the most active star-forming regions in the Large Magellanic Cloud. We want to determine the nature of the diffuse X-ray emission and improve our understanding of its origin including related interactions with the cold interstellar medium. Methods. We analyzed the diffuse X-ray emission observed with the extended Roentgen Survey with an Imaging Telescope Array (eROSITA) on the Spectrum-Roentgen-Gamma mission to determine the physical properties of the hot diffuse X-ray emission. Four spectral extraction regions were defined based on the morphology of the X-ray emission. We also studied HI and CO data, as well as Hα line emission in the optical, and compared them with the properties of the diffuse X-ray emission. Results. The X-ray emission in the four regions is well fitted with an absorbed model consisting of thermal plasma models (vapec) yielding temperatures of kT = ~0.2 keV and kT = 0.8–1.0 keV. The comparison of the X-ray absorption column density and the hydrogen column density shows that the X-ray dark lane located north of N11 is apparently caused by the absorption by HI and CO clouds. By estimating the energy budget of the thermal plasma, we also investigated the heating mechanism of the X-ray emitting plasma. The energy of the diffuse X-ray emission in the superbubble which is a star-forming bubble with a radius of ~120 pc including OB associations LH9, LH10, LH11, and LH13 can be explained by heating from high-mass stars. In the surrounding regions we find that the energy implied by the X-ray emission suggests that additional heating might have been caused by shocks generated by cloud–cloud collisions.