as variant (if exclude empty string in Last_Loaded_Date - it also possible, so check with debug what You have as input), but also
You have missed the space between ' and and
context.Query_string="select date_key,inc_date from date_dim where inc_date >'" +TalendDate.formatDate("yyyy-MM-dd",TalendDate.parseDate("dd-MM-yyyy",context.Last_Loaded_Date))+"'and inc_date < now()";
this is make date like - 2015-01-01and which is unparseable
context.Query_string="select date_key,inc_date from date_dim where inc_date >'" +TalendDate.formatDate("yyyy-MM-dd",TalendDate.parseDate("dd-MM-yyyy",context.Last_Loaded_Date))+"' and inc_date < now()";