Why does “today’s lesson” seem to be possessive?

possessives apostrophe saxon-genitive orthography

As many have said in comments, it is a genitive construction, but not strictly possessive. Compare by rewording, replacing the 's with for/of:

  1. I'll have to wait for an hour at the airport (or a wait of an hour)
  2. The lesson for today
  3. The programme of yesterday
  4. Groceries for two weeks.

Related

Difference between "inflection" and "inflexion"?
American English without an accent
Who do I need to send product information to? [closed]
Should I use present or past tense when referring to a (scientific) paper? [duplicate]
Usage of "ever" in a negative statement
Setup a Git server with msysgit on Windows [closed]
mingw-w64 threads: posix vs win32
Can I run multiple programs in a Docker container?
How to organize large R programs?
Is there a way to measure how sorted a list is?
What's the difference between buildscript and allprojects in build.gradle?
How can we redirect a Java program console output to multiple files?