Effect of Lying on Fasting

First of all, we would like to stress that telling lies is a bad conduct. It is not proper for righteous people and true believers; rather, it is an aspect of hypocrisy, as the Prophet (peace and blessings be upon him) said: “The hypocrite has three characteristics: he tells lies, breaks his promise and breaches trust.” (Reported by Al-Bukhari and Muslim)
Also, Allah Almighty says, (Only they invent falsehood who believe not Allah’s revelations, and (only) they are the liars.) (An-Nahl: 105)

Focusing on the question in point, we would like to cite for you the following Fatwa:

Al-Bukhaari reported that Abu Hurairah (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings be upon him) said: “Whoever does not give up false speech and acting upon it, and ignorance, Allah has no need of him giving up his food and drink.”
The phrase “false speech” includes lying, backbiting, spreading slander and bearing false witness, and every kind of speech that is haram.
Al-Hafiz said: With regard to the phrase “Allah has no need of him giving up his food and drink”, Ibn Battaal said: This does not mean that he is to be told to stop fasting, rather it is a warning against false speech and the other things mentioned along with it. This is an indication that (his fast) is not accepted. What is meant is that a fast that is contaminated with falsehood is rejected and that a fast that is free of that is accepted.
Ibn al-‘Arabi said: The aforementioned hadith implies that whoever does things mentioned here will not be rewarded for his fast. What is meant is that the reward for fasting cannot outweigh the sin of false speech and the other things mentioned here.
What is meant is that all sins have an effect on the fast and thus reduce the reward for fasting. The reward may be cancelled out altogether if there are too many sins.
Thus, the person who is accustomed to lying has to continue to strive against himself until he gives up this evil habit. Every time he sins, he should repent and seek forgiveness, for the one who repents from his sin is like the one who did not sin at all.