Yes Lazy approval will work with external email addresses even if there is not matching account in the domain or sharepoint profile.

You could also connect an external user with a Nintex Live account to allow them to use Nintex Mobile.

The lazy approval is working for domain users perfectly. For external users or non domain users, not able to get the response in the task. 

Any pointers.

Avinash - not sure if you solved your problem, I had a similar issue, internal worked but not external. In the end, steps I took to get external lazy approval working were:

1. Ensure that mail server can forward addresses from external to internal sharepoint (in my case the domain was set wrong)
2. In central administration configure Nintext Workflow Global Settings to send from an email address that can be sent to externally
3. In central administration configure Nintex Workflow LazyApproval settings with the same email alias as the reply to address in step 2 above.