MySQL 5.6 replication causes 'waiting for table lock' All of the sudden queries on slave server stopped with status "Waiting for table level lock"

I restart mysql service and stop replications and locking does not show up anymore. Once I turn replications back on I see huge increase in "waiting for table level lock" status for queries (show full processlist)

Replication is crucial for our situation and we can't keep it turned off.

What might cause this problem? Replication was running fine for last 5 months or so.

MySQL 5.6
It is possible that current replication thread is taking a lot of time updating a (big) change to a (big) table causing a long lock on the table. You may want to examine what the sql thread is trying to execute using mysqlbinlog with --start-position parameter. Hope this helps.