The question needs to be asked of yourself, why are you lying? Do you not want to hurt his/her feelings? Or is it because you are hiding something? Or is it because you know it will cause an argument and it's just easier to tell a little white lie? Once you work out the why, it is much easier to work out how to stop it and I completely believe that lying, no matter how small it is, is destructive to the relationship.
All the reasons for lying can be fixed, some more drastically than others, but nonetheless can be removed from a relationship. If your partner is lying to you, most people forget, that it can sometimes be because of the way you handle certain situations.
But as I say figure out the why and the problem becomes a lot easier to solve.