الحمد لله رب العالمين، وصلى الله وسلم على نبينا محمد وعلى آله وأصحابه أجمعين، أما بعد
With regards to supplicating generally on Laylatul Qadr, then it is a highly recommended act which is established from the Sunnah. The specific wording for the supplication during this night as is found in the Sunnah has has been reported on the authority of ‘Aa’ishah (radhiyallaahu ‘anhaa) who said, I said: “O Messenger of Allaah! What if I knew which night Laylatul Qadr was, what should I say in it?”
The Prophet (sallallaahu ‘alaihi wa sallam) said:
((you should say:
اللَّهُمَّ إِنَّكَ عَفُوٌّ تُحِبُّ الْعَفْوَ فَاعْفُ عَنِّي
(Allaahumma innaka ‘afuwwun tuhibbul ‘afwa fa’fu ‘annee)
O Allaah; You are The One Who pardons greatly; and You love to pardon; so pardon me.))
Ibn Rajab (rahimahullaah) said:
“Al-‘Afuww (The One Who pardons greatly) is from The Names of Allaah The Most High; and He overlooks the wrongdoings of His servants, He is The One Who erases their trace from them. He Loves to pardon; and so He Loves to pardon His servants, He likewise Loves from His servants that they should pardon each other, so if they pardon each other; He conducts His pardon with them; and His Pardon is more beloved to Him than His Punishment.”
The Wisdom Behind Asking For Pardon on This Night
Ibn Rajab said also:
“Indeed, he [i.e. the Prophet (sallallaahu ‘alaihi wa sallam)] commanded with asking for pardon on Laylatul Qadr, this being after the striving hard in actions within it and within the final ten nights. This is because the acquainted ones strive in performing actions, yet do not see any good deeds for themselves – not in circumstances nor in statements. So they return back to requesting pardon just like the circumstance of the sinner who falls short.
Yahyaa bin Mu’aadh said:
‘The acquainted one is not the one whose outmost objective in hope isn’t to obtain pardon from Allaah.’”
The Wisdom Behind Not Knowing Which Exact Night Laylatul Qadr Falls Upon
Ibn Qudaamah Al-Maqdisee (rahimahullaah) said:
“Some of the people of knowledge said:
Allaah The Most High made this night unapparent (obscure) upon the Ummah in order that they should strive hard in seeking after it; and that they should find aspiration in worship when seeking to attain it.
Just as He made the hour in which the supplication is answered on a Friday as unapparent – in order that they should be plentiful in making supplication throughout the day.
Just as He has made His Greatest Name unapparent from amongst His Names; and His Pleasure in varying forms of obedience – in order that they should strive hard in all of them.
Likewise He has made death and the establishment of The Hour as unapparent – in order that the people should earnestly endeavor in performing actions – out of caution from them both.”
 Reported by At-Tirmidhee (no.3513) and Ibn Maajah (no.3850) and Ahmad (no.25384) and others and was declared saheeh (authentic) by Shaikh Al-Albaanee in his Saheeh Sunan At-Tirmidhee (no.3513).
 Lataa-if wal-Ma’aarif p.279.
 Lataa-if wal-Ma’aarif p.280.
 Mawsoo’ah Al-Fiqhiyyah vol 35 p.366 original reference can be found in Al-Mughnee vol 3 p.117.
جزاكم الله خير, Very beneficial