The manager of a Grand Union supermarket in Montgomery County was shot in the back and killed last night after being ordered to lie on the floor by robbers who held up the store.

County police said they knew of no provocation for what some of them described as the execution-style shooting of the store manager, identifed as Robert D. Lamp.

The killing at the store in the Hillandale section came 14 hours after a county policeman and a private security officer were shot to death by burglars at a discount store about 1 1/2 miles away. Police said there was no indication of a link between the incidents.

Last night's incident began a few minutes before 9 p.m. when two robbers entered the supermarket in the Hillandale shopping center near New Hampshire Avenue and the Capital Beltway.

Only one checkout line was open, and no more than eight or 10 customers were in the store at the time the robbers arrived. One of the holdup men, who carried a handgun went to the cashier and took money from her cash register. He also robbed a male customer who was standing at the checkout counter.

Then, according to police, the gunman went to the manager's raised office at the front of the store, where he was joined by the other robber.

Lamp was ordered to lie on the floor. After he complied, policed said, he was shot in the back.

In a brief statement shortly after the shooting, police said they knew of no provocation for it. Early this morning, after hours of investigation, police said they still knew of no motive for the fatal shot.

Investigators said the store's safe in the manager's office apparently had been open when the robbers entered the store. Police said they did not know whether any money had been taken from it. The amounts taken from the cashier and the customer was undetermined.

Little panic or alarm was reported among the customers or the four or five store employes on duty at time of the robbery. No voices were raised during the entire incident, witnesses said.

After the shooting the two robbers fled from the store and joined a third outside before witnesses lost sight of them.

Police flooded into the area, lights flashing on the roofs of their cruisers. Officers began a house to house search, but as of early this morning, no suspects had been found.

Rescue workers also were sent to the scene, but it was quickly determined that Lamp was already dead.

Lamp, 28, years old, had recently moved to New Freedom, Pa., a small town near the Maryland border in York County.

The store in which last night's shooting occurred, just outside the Beltway at the New Hampshire Avenue exit, is no more than a few hundred yards from a Safeway store at 10171 New Hampshire Avenue that was held up last Saturday in an incident in which a store employe was shot and several persons were herded into a cooler.

Police expressed doubt last night that the Safeway holdup was connected to either of yesterday's fatal shooting incidents. They said descriptions and methods of operation of the suspects differed in all three incidents.