How are lamport clocks implemented in real world distributed systems?
Amazon's Dynamo [1] 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 [2] and Voldemort [3].

[1] G. DeCandia et al.: Dynamo: amazon's highly available key-value store. SOSP 2007:205-220

[2] http://basho.com/riak

[3] http://www.project-voldemort.com