In the previous verse (Lamentations 2:18) Zion is summoned to pray day and night.
In Lamentations 2:19 the focus is on the crying out to the Lord during the night: Arise, cry out in the night, at the beginning of the night watches!
Zion should give itself wholly to petition—not only during the day, but also during the night. She is told to arise from her bed as the need for earnest prayer is so pressing that it must take precedence over sleep.1
The prayer must continue at the beginning of the night watches.
The twelve hours of the night were divided into three watches of four hours each. The first watch began at sunset. There was also a middle watch (see Judges 7:19) and a morning watch (see Exodus 14:24). It could mean that they should pray at the beginning of the first watch only, or at the start of each watch which would imply praying throughout the night.2 When taking the call for urgent, continuous prayer into account, this is rather to be understood as implying renewed effort at the beginning of each watch (see Psalm 63:6). The urgency leaves no room for sleep at all, but calls them to be earnest as watchmen,3 seeking God at every moment for relief.
19 “Arise, cry out in the night, at the beginning of the night watches! Pour out your heart like water before the presence of the Lord! Lift your hands to him for the lives of your children, who faint for hunger at the head of every street.”