Can I change my address online?
No in LIC it is not possible.
Is there any Address change form which I can download online and submit the same to LIC Office?
There is no specific form for the change of address. You can write a simple application for change of address to Branch Manager, LIC of India.
You can submit this application via your LIC agent or you can visit nearest LIC branch. You can also send this application via normal post to the concerned LIC branch

Remember if you have policies from different branches you should send your request to respective LIC offices