Strictly my opinion -

Your bad lobe is one of the cam lobes that operates two lifters, so it,
or its companion will be the first to go in a marginal lubrication
situation. The lobes depend on oil thrown from the crankshaft cheeks -
some thing that I don't think happens for a couple of minutes after a
cool start - and especially with a cold engine.

It isn't a question of how quickly does the oil pump get oil get to the
cam bearings as journal bearings will retain enough oil to allow them
to be starved for a minute or two and oil gets there in a few seconds
anyway.

More critical though is how quickly does the crankcase develop that
general fog/spray of oil to finally lubricate all the miscellaneous
(and expensive) surfaces such as cam lobes and cylinder bores. The cam
is at the top of the engine & the lobes are the last thing to get lube.
Possibly if the crank is turning too slow, gravity is such that thrown
blobs of oil can't even make it to the lobes until the oil; gets really
thin. Remember that a new engine will inherently have considerably
less oil leakage from the bearings.

That's why preheat is so important to a Lycoming engine. It isn't as
though it is someting that should be done (usually). It is something
that must be done religiously every time (especially with summer weight
oil) as once cam surfaces are scratched, failure isn't far away. The
longer an engine has been sitting, the more the need for preheat. The
newer the engine, the more the need for preheat too. When and how
much? Who knows.

Also - thick oil reduces the flow demand of the engine, and more of it
will simply blow over the relief valve. Oil that is bypassed this way
has no access to the heat of the engine. Oil warmup will be slow even
if the CHT is getting into an operating range.

My guess is that there was a cold start or cool start with summer oil
combination somewhere in its history although you indicated you always
preheated. Or maybe the cam which is supposed to be case hardened
isn't as hard as it should be. You might check the cam hardness with a
new file on another lobe. It should not be able to bite into it. If
it does, get a hardness test done on it.