Is it possible to use LimeSurvey for dual assessment. For eg, employee performance assessment.

The employee assess himself with a set of questions. His supervisor assess the employee with the same set of questions.

We need to store the both data in the same survey for comparison.

You should be able to do that with tokens. Place the "employee number" in a custom attribute.

I assume you mean sending individual invites to employee and supervisor. And compare the results with employee number with a custom page.

Yes, I assumed you would be doing the comparisons with a post-survey analysis tool like SPSS or R.