@Sairam_pera
IMO, Search and Filter will not provide any performance benefit over LookUp.
Filter and Search return multiple records whereas LookUp is specifically designed to return a single record. Therefore, LookUp will be the more performant of all these functions.
Also, if you're using SharePoint, Search is not delegable. Therefore, Search will not return the correct record if the data source contains more than 2000 rows.
The typical reason for slow performance is that the data source contains many columns which will slow down data retrival.
If you're using SharePoint or SQL, you can try indexing the DocumentCode and CaseId columns. That might help to improve the retrival time from within the data source.