Mystery still surrounds the unsolved murder of the prominent local politician, who was a member of Chancellor Angela Merkel's centre-right Christian Democratic Union (CDU) party.
The 65-year-old was shot in the head at close range on the terrace of his home in Kassel, around 160 kilometres northeast of Frankfurt, just after midnight on Sunday, June 2nd.
At his funeral service held in the Martinskirche in Kassel, state government head Bouffier, also of the CDU party, said: "It is a sad, painful and almost incomprehensible occasion that brings us together.”
More than 1,300 people came together to bid farewell to Lübcke, who led the district government in Kassel, reported Spiegel.
In an emotional ceremony, Christoph Lübcke, one of the CDU politician's two sons, said: "Dear Papa, we must say goodbye to you today after your inconceivable death."
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The nation has been left shocked by the brutal murder of the politician, who was vocally pro-migrant.
Investigators say it is still unclear why Lübcke was killed, but a possible political motive has not been ruled out, given the politician had previously received numerous death threats.
At the service Lübcke was remembered for his positive contribution to the community in Kassel.
Bouffier said: "Today, we remember Walter Lübcke first and foremost as a human being.”
Police and the Bundeswehr (German army) held an honorary guard at Lübcke's coffin.
A white rose lies on the coffin. Photo: DPA
Online hate posts
However, the circumstances of the politician's death could not be ignored.
"With the cruelty of the deed comes the uncertainty,” said Martin Hein, bishop of the Protestant Church of Kurhessen-Waldeck. “Who was it that put an end to this life in cold blood?"
Members of the German government last week slammed online hate comments cheering the unsolved murder of Lübcke.
Hein addressed the online commetns at the funeral, saying that Lübcke's dignity must be respected, including on the internet.
Flags of mourning
On Thursday government buildings across Hesse flew flags at half mast out of respect for Lübcke.
Meanwhile, inquiries are continuing into Lübcke's death.
Investigators are looking into 213 tip-offs and lines of inquiry, according to the state criminal investigation office.