Does SSMS follow the same support lifecycle as SQL Server? I've found information about the support lifecycle for SQL Server (such as this page for SQL Server 2008/2008R2), but haven't found any information about SSMS. Does SSMS follow the same support lifecycle?
In the past, the releases lined up - each new SQL Server was accompanied by a new Management Studio. 

However, in June of 2015 (concerning SQL Server 2016 and onwards) MS announced separate life cycles:


  With the release of SQL Server 2016 Community Technology Preview (CTP)
  2.1, customers can for the first time experience the rapid preview model for their on-premises SQL Server 2016 development and test
  environments and can gain a faster time to production.     
  
  In addition, we are delighted to announce our first “preview” release
  of SQL Server Management Studio!  This is our first effort to release
  SQL Server Management Studio (SSMS) in a mechanism outside of the SQL
  Engine releases.  Our goal is to update this frequently with new
  features, fixes and support for the newest SQL Server features in SQL
  Server Engine and Azure SQL Database.


From the MSDN Blog on SQL Server Releases.



Based on your edit to be about support life cycles, I'm not sure that question has an answer since this new direction has been implemented (concerning future releases). As for past SSMS releases, I don't think I know of any updates or support to SSMS after the corresponding SQL Server version has been phased out - so I'd say it's safe to assume they align.