Sadly, this is not mathematics. Else, I'd concur that the designation
"lower bound" should be accurate with respect to a certain set.

I fail to see what is missing in the explanation "the lowest value is a
lower bound *in a typical case*". It allows for lower execution times.

Also, your suggested wording "the lowest value is an upper bound" is
certainly not more accurate, if not an oxymoron in itself. I repeat,
what you usually want when timing code snippets is the execution time
under realistic conditions, because you'd have a hard time defining what
"the fastest machine" is.