Can anybody advise on how to remove the key lookup costing 48.1%
Is it a theoretical question or this plan performs slowly?
To avoid Lookup you should add the lookup fields (you may find them in the Output property of the Key Lookup operator) into the index IX_CaseActivity_1.
However, if there is a real performance problem, the cost might not be an indicator of the plan bottleneck. The cost is based on the estimates, if the estimates are wrong the cost is also wrong. To determine the wrong estimates you should get the actual plan and compare actual and estimated row count. If you find huge difference – find the bottom most operator that has these difference, and it would be a good starting point to address the plan problem.