On a Lycoming 360 the magic number is 380F, below this temp research shows that power changes and sudden cooling does not harm the engine.
Above 380F is the danger area, only change one of anything that cools the cylinder heads. i.e. Do not reduce power, richen the mixture and increase airspeed together, will crack the heads over time.
Forget Lycomings max 480F cylinder head temp, this is an absolute red line
it may run, but wont last long.
Cruise temps should be 380f or less for long life and above 400f in climb are into the danger area. Best if in all modes of operation temps stay 380f or less.
Point of LOP is not just saving fuel, but keeping cylinder head temps low using air rather than expensive fuel. Matched fuel flow for each cyl is required to do this see GAMI injectors. Difficult to do with a carb.
Lycoming did issue a service bulletin to reduce timing on 360 from 25 to 20 degres this reduces cyl head temps and does not affect power as over timed anyway.
Note Running at Max EGT is not the max power point, it is 125f down on the rich side of peak.
Lycoming say at 65% power no damage can done by any cooling or mixture changes. But Lycoming do say that any damage to one of their engines is down to the operator not their design and manufacturing faults which are many.