What is the best way to remove key lookup (costing 68%) ?
I know that index with included columns will help, but wont it make the index (Clustered index) wider ?
It is 68% of the estimated cost of the query, according to the optimizer's standard model (which takes little account of whatever hardware you might be running SQL Server on).
The real question is whether this is a good execution plan for your query and system. From the information provided, it is hard to tell. Not only is the plan anonymized, it is an estimate – there is no post-execution data to tell us how accurate the optimizer's estimates were.
Whether this is a good plan or not depends heavily on how selective the existing nonclustered indexes are, and how many rows are actually looked up in the base table. Without a post-execution ('actual') plan, and an indication of how representative the execution is of your workload, it is really tough to offer guidance.
Are you experiencing a performance problem with this query, or just concerned by the apparently-high percentage cost of the Key Lookups?
The thing is, each lookup is returning a large number of columns – 24 for the first one and 76 for the second. It is unlikely your want to include so many columns in the existing nonclustered indexes. It also raises questions about the database design. Again, this depends on information (table and index DDL) that isn't available to us from the anonymized plan alone.
In summary, if the optimizer's estimates are reasonably accurate, this is likely a good execution plan for your query. If the estimates are not accurate, you should do all you can to make them accurate (perhaps by updating or providing new statistics). If you can provide more context and information to work with, we will likely be able to offer more specific advice.