Context : Asymptotic giant branch ( AGB ) stars are cool luminous evolved stars that are well observable across the Galaxy and populating Gaia data .
They have complex stellar surface dynamics , which amplifies the uncertainties on stellar parameters and distances .

Aims : On the AGB star CL Lac , it has been shown that the convection-related variability accounts for a substantial part of the Gaia DR2 parallax error .
We observed this star with the MIRC-X beam combiner installed at the CHARA interferometer to detect the presence of stellar surface inhomogeneities .

Methods : We performed the reconstruction of aperture synthesis images from the interferometric observations at different wavelengths .
Then , we used 3D radiative hydrodynamics ( RHD ) simulations of stellar convection with CO5BOLD and the post-processing radiative transfer code Optim3D to compute intensity maps in the spectral channels of MIRC-X observations .
Then , we determined the stellar radius using the average 3D intensity profile and , finally , compared the 3D synthetic maps to the reconstructed ones focusing on matching the intensity contrast , the morphology of stellar surface structures , and the photocentre position at two different spectral channels , 1.52 and 1.70 \mu m , simultaneously .

Results : We measured the apparent diameter of CL Lac at two wavelengths ( 3.299 \pm 0.005 mas and 3.053 \pm 0.006 mas at 1.52 and 1.70 \mu m , respectively ) and recovered the radius ( R = 307 \pm 41 and R = 284 \pm 38 R _ { \sun } ) using a Gaia parallax .
In addition to this , the reconstructed images are characterised by the presence of a brighter area that largely affects the position of the photocentre .
The comparison with 3D simulation shows good agreement with the observations both in terms of contrast and surface structure morphology , meaning that our model is adequate for explaining the observed inhomogenities .

Conclusions : This work confirms the presence of convection-related surface structures on an AGB star of Gaia DR2 .
Our result will help us to take a step forward in exploiting Gaia measurement uncertainties to extract the fundamental properties of AGB stars using appropriate RHD simulations .