This is the first paper of a series devoted to the Lambda Orionis star-forming region, from the X-ray perspective, which will provide a comprehensive view of this complex region. In this paper we focus in uncovering the population of the central, young cluster Collinder 69 (C69), and in particular those diskless members not identified by previous near- and mid-infrared surveys, and to establish the X-ray luminosity function for the association. We have combined two exposures taken with the XMM-Newton satellite with an exhaustive data set of optical, near- and mid-infrared photometry to assess the membership of the X-ray sources based on color-color and color-magnitude diagrams, as well as other properties, such as effective temperatures, masses and bolometric luminosities. We detected a total of 164 X-ray sources, of which 66 are probable and possible cluster members. A total of 16 are newly identified probable members. The two XMM-Newton pointings east and west of the cluster center have allowed us to verify the heterogeneous spatial distribution of young stars, probably related to the large scale structure of the region. The disk fraction of the X-ray detected cluster sample is very low, close to 10%, in remarkable contrast to the low-mass stellar and substellar population (mostly undetected in X-rays) where the disk fraction reaches about 50%. The X-ray luminosity function of C69 provides support for an age of several Myr when compared with other well known young associations. With our improved cluster census we confirm previous reports on the untypically low disk fraction compared to other clusters of several Myr age. The different disk fractions of X-ray detected (essentially solar-like) and undetected (mostly low-mass stars and brown dwarfs) members can be understood as a consequence of a mass-dependence of the time-scale for disk evolution.
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