Beginning with what you wrote, after a few trials and errors I ended up with the following which gives what I meant:
\definenumber[ReverseNumberOrder][numberorder=reverse]
\defineenumeration[Lecture]
[location=hanging,
text={Lecture n° {\convertednumber[ReverseNumberOrder]}.},
between=,
before={\incrementnumber[ReverseNumberOrder]},
number=no,
after={\hrule\blank}]
\starttext
\startLecture Tuesday December 6th: Banach spaces.
\startitemize[n]
\item First subject.
\item Second subject.
\stopitemize
\stopLecture
\startLecture Tuesday November 29th: Norms.
\startitemize[n]
\item First subject.
\item Second subject.
\stopitemize
\stopLecture
\startLecture Tuesday November 22nd: Topological Vector Spaces.
\startitemize[n]
\item First subject.
\item Second subject.
\stopitemize
\stopLecture
\stoptext