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The burning lamb was spotted dumped on the front door step of a Corstorphine home by neighbours, and police were called to the Clermiston Ave property at 1.30am.
Andrew Naziris (28) said he had no idea about the incident until police knocked at his door, He found the gruesome charred carcass of Larry the lamb, who normally lived tethered at the rear of his property.
The lamb's head had been crushed and it had substantial burns to its body, Constable Brent Mitchell said.
''Whether it was alive or dead when it was burnt, either way it has met a fairly cruel and unnecessary way to die.''
The lamb was the family pet of Matt Johnston (28), and his young daughter ''absolutely loved him, loved him to bits''.
''It is absolutely horrible.''
Larry, who spent is first few weeks living inside and was regularly bottle fed by his daughter, was to turn one in September.
He was yet to tell his 2-year-old daughter about the incident, as ''they were best friends''.
''Larry is a member of our family, and I think it is absolutely horrific what they have done. We are after justice.''
Police had evidence indicating the lamb ''may have been taken to a nearby address where there was a group of people who may have been drinking''.
That evidence indicated the sheep may have been taken to the party, before being returned to its home, he said.
''We have spoken to some people at the party and they claim to have no knowledge of the incident,'' Const Mitchell said.
There was no known ''bad blood'' between individuals, he saidPolice took cruelty to animals seriously and anyone with information was urged to contact their nearest police station.