Can anyone explain, how lamport clocks implementations are used in modern distributed systems? Can you name an open source package which implements this algorithm?
Amazon's Dynamo  is a distributed storage system that uses vector clocks "to capture causality between different versions of the same object". Section 4.4 of the paper describes how exactly Lamport clocks are used to manage data versioning.
Some of the open source implementations of Dynamo are Riak  and Voldemort .
 G. DeCandia et al.: Dynamo: amazon's highly available key-value store. SOSP 2007:205-220