What binary log format are you using ? Are you using ROW or STATEMENT ?
SHOW GLOBAL VARIABLES LIKE 'binlog_format';
If you are using ROW as a binlog format make sure that all your tables has Primary or Unique Key:
SELECT t.table_schema,t.table_name,engine
FROM information_schema.tables t
INNER JOIN information_schema .columns c
on t.table_schema=c.table_schema
and t.table_name=c.table_name
and t.table_schema not in ('performance_schema','information_schema','mysql')
GROUP BY t.table_schema,t.table_name
HAVING sum(if(column_key in ('PRI','UNI'), 1,0)) =0;
If you execute e.g. one delete statement on the master to delete 1 million records on a table without a PK or unique key then only one full table scan will take place on the master's side, which is not the case on the slave.
When ROW binlog_format is being used, MySQL writes the rows changes to the binary logs (not as a statement like STATEMENT binlog_format) and that change will be applied on the slave's side row by row, which means a 1 million full table scan will take place on the slave's to reflect only one delete statement on the master and that is causing slave lagging problem.