Lamentation is the ability to touch and express the deepest sorrows a human can experience, typically during a period of grieving the dead. Lamentation isn't one emotion, it's a constellation of emotions based on touching the core wish of "Please return me to a place where this event did not happen!"
Lamentation unlike sadness acknowledges the absolute horror of the event, without trying to predict or control the emotions or experience. Frequently, lamentation will include wailing and screaming. When we listen to a very sad song that as is a form of lamentation.
Lamentations were actually outlawed in Greek culture around 6 BCE (See Resource 1.) Where I live in the US, I can't imagine lamentation being expressed publicly; the funerals I've seen everyone is following a script where the only emotion that is allowed to be visibly displayed is sadness and the only expression of sadness that is allowed is quiet (or nearly quiet) crying.
Wishing to return to "a place where this event did not happen!" calls up a complex and complete set of emotions: anger, sadness, anxiety, panic, disbelief, denial, sadness, etc. Lamentation isn't an emotion, it's an experience, a direct outpouring of sorrow.
Lamentation is the end expression of unlimited sorrow and should be viewed as a requirement for ecstasy.
Resources
On Ancient Greek Lamentation and Women In Democracy
The Ritual Lament in Greek Tradition - Margaret Alexiou