Why is the backup sizes of AlwaysON replicas different?
The size of the database is always exactly the same on both primary and secondary replicas. The difference you are noticing on the backup file size could be because one of the two reasons


You didn’t use compression on secondary and applied compression when you took the backup on primary server. 
As you already mentioned you were using Dell Lite Speed, which has different algorithm and compression level which also make a difference in your backup file size.  


The performance issue could be because of different reasons. After you restore the database, make sure to check and if necessary to update the statistics, Index fragmentation level, and the query plan cache which usually has significant performance influence after a database restore.