It is true what they say, "you need a thousand lies to cover up one lie" and sometimes it really is not worth it. In certain situations, telling a small white lie doesn't seem like a big deal but in the long run, it brings nothing but hurt.
It is better to tell them that you are not interested rather than dangling them till eternity. It might hurt them in the beginning but they will thank you for your honesty.
It might seem harmless to tell the other person that you are breaking up for family reasons but the person deserves to know the truth. So be bold enough to tell the real reason behind the breakup.