The comments, anecdotes, and historical context he gives the papers are by themselves a great read, especially if you're even somewhat familiar with the results. The comments on #12, which introduces the Bakery Algorithm [1] are a great example of this.
"What Good is Temporal Logic?" (https://lamport.azurewebsites.net/pubs/pubs.html#what-good) is in the running for my favorite CS paper. Well worth reading, and understandable even if you have a passing familiarity with predicate logic.
This page make me want to write some narratives about my own papers. Maybe I wouldn't release the narratives, but Lamport's page made me realize how much detail is lost to time. The context of the papers is interesting and maybe even relevant to the research.
Interesting how that makes me think of state in programming. Maybe theres a way to encapsulate state in these papers to capture as much as possible from the context.
* On the oft-misunderstood significance of the bakery algorithm: https://lamport.azurewebsites.net/pubs/pubs.html#bakery
* On submitting an algorithm with a bug in it, thus arousing interest in verifying concurrent algorithms (culminating decades later in the development of TLA+): https://lamport.azurewebsites.net/pubs/pubs.html#proving
* On how nobody has actually read his most famous paper (Time, Clocks...): https://lamport.azurewebsites.net/pubs/pubs.html#time-clocks
* Hanging out, drinking beer at Dijkstra's house: https://lamport.azurewebsites.net/pubs/pubs.html#new-approac...
* On creating the first (impractical) digital signature algorithm: https://lamport.azurewebsites.net/pubs/pubs.html#dig-sig
* A several-times-rejected paper which then became one of the most cited in the field of temporal logic: https://lamport.azurewebsites.net/pubs/pubs.html#sometime
* A lifelong source of fascination, the arbiter problem: https://lamport.azurewebsites.net/pubs/pubs.html#buridan
* The creation of LaTeX: https://lamport.azurewebsites.net/pubs/pubs.html#latex
* On presenting the first paxos paper in an Indiana Jones outfit, to widespread incomprehension: https://lamport.azurewebsites.net/pubs/pubs.html#lamport-pax...
I'll stop here because basically every single summary is fun and worth reading.