UPDATED: NOVEMBER 12TH 2018
Most good clubs in Liverpool stay open late until 4-6am, even most bars in Liverpool stay open until 3-4am.
Opening times will vary from venue to venue, and depending on what night it is, though generally, everywhere is open late over the weekend, especially on Saturday nights as Liverpool's late night clubs stay open till 7am.
If you're a pub drinker, the opening hours are a little more strict as 12:30-2am is usually the closing up hours. Though again, depending where you are, I was in the Grapes pub on Mathew Street one Saturday night which was open till 4am — The trick is to follow the crowds and music while ignoring the people waiting for taxis.