At the European Laboratory for Particle Physics (CERN), commercial greases and oils are extensively used to lubricate moving devices operating in high-radiation areas, absorbing doses up to the MGy range. Due to their sensitivity to radiation, lubricants can become fluid or solid in operation, potentially causing component failures and compromising the operation of the accelerator complex. CERN is therefore developing methodologies to select radiation tolerant commercial lubricants for critical Beam Intercepting Devices (BIDs) such as high-power targets, dumps and collimators. A careful selection of greases is fundamental to reduce the risk of failure, to optimize equipment lifetime and to minimize maintenance and unwanted radiation exposure of personnel in high radiation areas. Three different parameters are considered to select commercial lubricants: the expected total dose absorbed in operation, the maintenance feasibility and the failure impact in terms of accelerator downtime and of personnel involvement in replacement procedures. Based on these criteria, an example of relevant application is presented: the lubrication of the new internal beam dump of the Super Proton Synchrotron (SPS). Experimental radiation damage data allowed the identification of two radiation tolerant commercial greases to lubricate the dump support jack assembly.