Hello ,
I am able to resolve this . Writting below the steps of self service deployment from sandbox to production env.
1. Login to LCS and open the sandbox env detail page .
2. Go to Maintain tab and apply update option .
3. Select the latest released package and click on apply .
4. Check the status of application deployable package in environment history detail page there .
5. After the status is completed, Click on the signed off link and Mark as release candidate link there .
6. Now open the Production env detail page
7. Click on maintain tab and click on update environment option there.
8. package with mark as release candidate will appear there .
9. Select the downtime to schedule the deployment and click on OK.
10. Deployment will start and page will be in Service mode . Status will change to deployed after deployment completed.