The man had been arrested on suspicion of criminal damage to the decorations in Morecambe Road in the early hours of last Monday.
CCTV was passed to the police which showed a man slashing inflatables and laser cables with a knife.
Sgt Adie Knowles of Morecambe Police said the man will now have to pay compensation to the family or face court action.
Sgt Knowles said: “After careful consideration and liaison with the aggrieved party the male was issued a conditional caution where one of the conditions is to pay compensation to the aggrieved.
“If these conditions are not adhered to then the man will be summonsed to appear at court.
“We would like to thank the public with their assistance in this case.”
The display was put up by Denver Peel and his wife Kirsty to entertain their two children and local residents.
Denver said they had spent around £3,000 on inflatables and other decorations to adorn the front garden of their home.
He said dozens of children and motorists had been stopping to admire the festive scene and take photos.
The vandalism took place at around 1am while Denver, his wife Kirsty and their children, three-year-old Dougie and four-year-old Brooklyn, were all in bed.
Police do not name people who have been cautioned for an offence since is not a criminal conviction (being found guilty in court), although it is recorded on your criminal record.