What are the conditions for the percentage power vs fuel consumption figures in the engine operator manual?
The correct source for burn data is not the Lycoming operator manual, but the aircraft manufacturer's manual.

All modern POH have the consumption data qualified (in tables) relative to altitude and temperature.

When adding a new plane to our fleet, we enter that data in and do a linear regression on the data, so that we have a generalized equation for flight planning purposes.

You need to look at the aircraft documentation, not the engine documentation, because the same engine in different planes will have different performance. The POH will have figures which were established empirically, by the manufacturer's test pilots. Fuel burn tests are conducted at various altitudes, and temperatures.

Please note that to answer your fuel burn questions, it is essential to know the aircraft, configuration, and really, have that specific POH.  Then the questions you pose are readily answered.