In order to answer some of the major open questions in the fields of supermassive black hole (SMBH) and galaxy evolution, a complete census of SMBH growth, i.e., active galactic nuclei (AGN), is required. Thanks to the combination of the new deep all-sky surveys, such as those by the Wide-field Infrared Survey Explorer (WISE) and the Spectrum-Roentgen-Gamma (SRG) missions eROSITA and ART-XC, this task is now becoming feasible in the nearby Universe. We present a new survey, the Local AGN Survey (LASr), with the goal of identifying AGN unbiased against obscuration and determining the intrinsic Compton-thick (CT) fraction. As part of LASr, we have assembled the most complete all-sky sample of galaxies within 100Mpc from astronomical databases, four times deeper than the current local galaxy reference, the Two Micron All-Sky Survey Redshift Survey (2MRS), which turns out to miss ~20% of known luminous AGN. This galaxy sample will serve as parent sample to select AGN. We assemble and characterise all 4.3k known AGN within the volume and employ infrared colour selection to find new AGN candidates independent of their obscuration. The fact that none of these candidates have been detected by Swift/BAT yet indicates that the CT fraction is in the range of 40-55%. We estimate the efficiency of the infrared colour selection and use it to predict the total number of AGN in the volume, finding that a third of the objects are still undetected. Thanks to the deep flux limits, the all-sky surveys of eROSITA and ART-XC are going to detect many of these sources, while putting tight constraints on those that remain undetected and thus be CT. These X-ray information will be highly complementary to the infrared and help to overcome selection biases of the latter. Thus, the combination of infrared and X-ray selection of AGN is the best approach to obtain an unbiased and complete census of (significant) black hole growth in the local universe. Such a census will serve as redshift zero benchmark for AGN population studies, providing constraints on the AGN duty cycle, luminosity and accretion rate distributions and radiative efficiencies.