Stuart Brownhill, 59, was absent during a roll-call at 05:00 BST at the North Sea Camp prison, near Boston, police said.
He murdered Lynne Taylor while her 11-year-old son slept in their home in Werneth, Oldham, in 1984 and was jailed for life at Manchester Crown Court the following year.
Police have asked the public not to approach him.
More on this story and others news in Lincolnshire
Brownhill met Ms Taylor on a night out and later set fire to her home. He admitted he strangled Ms Taylor after trying to rape her and that he knew the boy was asleep in the property when he started the fire.
He is described as 5ft 8in tall, bald, and has a green right eye and a blue left eye. Officers believe he may be wearing a brown jacket and black boots.
The force have appealed for anyone who sees him to contact them immediately by dialling 999.
Officers said anyone with information on his whereabouts should call 101.

Members of the RMT union will walk out for 48 hours from Sunday 7 August, 24 hours on Thursday August 11 and over the weekend of 13/14 August.
The RMT is against the increased use of trains on which the driver opens and closes the doors at stations.
ScotRail has said such operations are already common on the network.
RMT general secretary Mick Cash said: "Recent rock-solid strikes on ScotRail have been supported by the travelling public who understand that the staff are fighting for the basic principles of rail safety.
"In spite of this, Abellio/Scotrail continue to ignore the strength of feeling amongst their staff and passengers over the extension of driver-only operation."
ScotRail says 59% of customers already travel on a train where the doors are safely opened and closed by the driver, and insists that the job, pay and conditions of conductors are guaranteed.
Phil Verster, managing director of Scotrail Alliance, has previously said: "This industrial action by the RMT is not about safety, it's not about a second person on a train and it's not about jobs or pay and conditions.
"It is about modernisation of the railway and preparing us for a railway that Scotland can be proud of for the next 40 or 50 years."
A convicted murderer has absconded from an open prison in Lincolnshire.
[NEXT_CONCEPT]
Workers on ScotRail are to stage a fresh wave of strikes in a long-running dispute over the increased use of trains without guards.