Laylat al-Qadr is understood to be one night towards the end of the month of Ramadan, but it is not clear which night it is.
Shi'i hadith specify the 19th, 21st, and 23rd as the strongest candidates for the night of Laylat al-Qadr. This is why there is special worship done all night on those days, and not usually on the later nights.
In the Sunni tradition, there is usually a focus on the later nights (any of the last 10 odd nights, but particularly the later ones) especially the 27th.
If one is a Shi'i, there is no harm in doing acts of worship for Laylat al-Qadr on the 27th of Ramadan, with the idea that it could possibly be a candidate for Laylat al-Qadr. Of course, acts of worship like Du'a Jawshan al-Kabir can be done any time.
Allah knows best.