We present the observed-frame optical, near- and mid-infrared properties of X-ray selected AGN in the Lockman Hole. Using a likelihood ratio method on optical, near-infrared or mid-infrared catalogues, we assigned counterparts to 401 out of the 409 X-ray sources of the XMM-Newton catalogue. Accurate photometry was collected for all the sources from U to 24um. We used X-ray and optical criteria to remove any normal galaxies, galactic stars, or X-ray clusters among them and studied the multi-wavelength properties of the remaining 377 AGN. We used a mid-IR colour-colour selection to understand the AGN contribution to the optical and infrared emission. Using this selection, we identified different behaviours of AGN-dominated and host-dominated sources in X-ray-optical-infrared colour-colour diagrams. More specifically, the AGN dominated sources show a clear trend in the f_x/f_R vs. R-K and f_24um/f_R vs. R-K diagrams, while the hosts follow the behaviour of non X-ray detected galaxies. In the optical-near-infrared colour-magnitude diagram we see that the known trend of redder objects being more obscured in X-rays is stronger for AGN-dominated than for host-dominated systems. This is an indication that the trend is more related to the AGN contaminating the overall colours than any evolutionary effects. Finally, we find that a significant fraction (~30%) of the reddest AGN are not obscured in X-rays.