وَ الَّذينَ إِذا فَعَلُوا فاحِشَةً أَوْ ظَلَمُوا أَنْفُسَهُمْ ذَكَرُوا اللَّهَ فَاسْتَغْفَرُوا لِذُنُوبِهِمْ وَ مَنْ يَغْفِرُ
الذُّنُوبَ إِلاَّ اللَّهُ وَ لَمْ يُصِرُّوا عَلى ما فَعَلُوا وَ هُمْ
And those who, when they commit an indecent act or wrong themselves, remember Allah, and plead (Allah's) forgiveness for their sins and who
forgives sins except Allah? and who do not persist in what they have
committed while they know.(3:135)
أُولئِكَ جَزاؤُهُمْ مَغْفِرَةٌ مِنْ رَبِّهِمْ وَ جَنَّاتٌ تَجْري مِنْ تَحْتِهَا الْأَنْهارُ خالِدينَ فيها وَ نِعْمَ أَجْرُ
Their reward is forgiveness from their Lord, and gardens with streams running in them, to remain in them (forever). How excellent is
the reward of the workers!(3:136)
In the book Nahjul Blaghah, there is a saying from Imam Ali (peace be upon him) about repentance:
Istighfar" (asking Allah's forgiveness) is meant for people of a high
position. It is a word that stands on six supports. The first
is to repent over the past; the second is to make a firm
determination never to revert to it; the third is to discharge all
the rights of people so that you may meet Allah quite clean with
nothing to account for; the fourth is to fulfill every obligation
which you ignored (in the past) so that you may now do justice with
it; the fifth is to aim at the flesh grown as a result of unlawful
earning, so that you may melt it by grief (of repentance) till the
skin touches the bone and a new flesh grows between them; and the
sixth is to make the body taste the pain of obedience as you
(previously) made it taste the sweetness of disobedience. On such an
occasion you may say "astaghfiru'llah".
There are some points regarding this Hadith:
Imam Ali (peace be upon him) deems six conditions for a true repentance. the first two are the basis of every repentance. the next two are the requisites for its acceptance and the last two are necessary for its perfection.
The third condition includes both belongings and rights. one has to make up for any right he/she has violated in the past.
The forth condition is about (to name but a few) compensating for ritual prayers one has failed to perform in their prescribed times or making up for the obligatory pilgrimage to Mecca one has failed to make in the past when he/she was physically and financially bale to do so.
If your lie has resulted in trampling others' rights, you have to make up for it by apologizing or doing anything to make sure that they have forgiven you.
If your lie has not resulted in violating anyone's right, taking the first and the second step of the above-mentioned Hadith is enough.