Lying about past or present (un)employment is grounds for termination. Or you will just fail the background check and not get hired.Why tell them you are unemployed? Just tell them that you are looking to "change jobs" because you want career progression and you think that you have the right transferable skills to succeed with this new company.
Why are make this complicated? It is a disadvantage to quit a job vs. sucking it up and finding one while still employed.