The three big papers: clocks [0], Paxos [1], Byzantine generals [2].

[0] https://lamport.azurewebsites.net/pubs/time-clocks.pdf

[1] https://lamport.azurewebsites.net/pubs/lamport-paxos.pdf

[2] https://lamport.azurewebsites.net/pubs/byz.pdf

Or, if you prefer wiki articles:

https://en.wikipedia.org/wiki/Lamport_timestamp

https://en.wikipedia.org/wiki/Paxos_(computer_science)

https://en.wikipedia.org/wiki/Byzantine_fault

I don't know that I would call it "solved", but he certainly contributed a huge amount to the field.

Lamport's website has his collected works. The paper to start with is "Time, clocks, and the ordering of events in a distributed system." Read it closely all the way to the end. Everyone seems to miss the last couple sections for some reason.