Replication from log shipping database
No. However, there are some capabilities supported with log shipping and replication on the primary. https://msdn.microsoft.com/en-us/library/ms151224.aspx

As Aaron stated, you could add an additional secondary. If you wanted to use replication to handle subsets of the primary data, or build out a better formatted reporting server (different indexes, subsets of data through filtering, etc), then I would recommend replicating from the primary. 

Hope this helps!