My specific engine is not listed in the Lycoming Engine Manual table of contents.

Many Lycoming engines are not specifically listed as Lycoming produces a general direct-drive engine manual that covers many engine models. A great reference is Service Letter 114 which shows which manual is applicable to your model of engine. This will be shown as “Part number”. For example, you can find the O-360-A1A in SL 114 and see that the associated “part number” (Parts catalog) is PC-106. Installation, Operation, Overhaul and Maintenance Manual part numbers are also shown in their respective columns.

Note: Lycoming is now naming the manuals so that your model/series of engine is obvious and this may eliminate having to reference Service Letter 114.