B737 Technician reported conflicting information regarding the correct lubricant to use during engine build up procedures resulted in aircraft operations in a non airworthy condition.

Narrative

On the night of DATE the ZZZ EBU (Engine Build Up) crew required additional lubricant referred to as Molykote G-N Assembly Paste in Engineering Authorization X rev I. After referencing Aircraft Maintenance Manual; it was determined that we had not been using the lubricant called out for in the Aircraft Maintenance Manual. Engineering has since verified that the Lubricant p/n DCGNK listed in the Engineering Authorization (full document) has been no longer approved for this task. The correct lubricant was not set up in our parts system and an ECRA (Engineering Change Request Authorization) generated to create an M&E number to start the process of procuring the correct lubricant. A couple of concerning issues are [the] Company did not discontinue the scheduling of these tasks except for ZZZ after an aircraft was deferred in lieu of performing the job without the required lubricant. A review of logs indicated other stations were still performing the task. To date the system is not set up with the correct lubricant and some of the stations show zero quantity of an aerosol spray that supposedly; can be used as a non-preferred application method. Not only non-preferred but also pointed out to local management near impossible to get the coating thickness requirements met on the required areas of the Fan Disk (pressure faces of the dove tail and the Booster Spool face where the blade dovetail contacts). While the Engineering Authorization is specific to which form of lubricant to use; the use of the non-preferred method; aerosol spray raises safety and health issues especially as most of these tasks are performed in an uncontrolled environment prohibiting suitable precautions to be taken. This; in addition to the quality consideration of the work accomplished.