I don't believe the above approach will work because there could be multiple Acquired/Lost combinations for a single Auid (sorry, should have explained that in my original post). For example, the result of the query when run against the records in the screenshot I provided is:

FirstAquireID=2

LastLostID=34

Auid=71127c4145a...

What I ended up doing (and still have more testing to do), is use a modified version of the what was explained in this article: http://www.sqlservercentral.com/articles/T-SQL/68467/

Using this method, I was able to flag and delete the unwanted rows from the staging table.