The 30-year-old scored four goals in 22 appearances for the Spitfires last season and spent three months on loan at Aldershot Town.
Lafayette has previously had spells with Welling, Woking and Luton Town.
Dover host Boreham Wood in the National League on Tuesday, having begun the 2016-17 season with a 0-0 draw at Wrexham on Saturday.
Find all the latest football transfers on our dedicated page.

The body of Paul Jefferies, 52, was found by police at his house in Coggins Mill Lane, Mayfield, on 25 February following concerns for his welfare.
A post-mortem examination showed he died from multiple injuries.
The boy, from Crowborough, who cannot be named for legal reasons, is accused of killing Mr Jefferies on 23 February. He has appeared before magistrates.
A 16-year-old boy and an 18-year-old man from Crowborough and a 17-year-old girl from Eastbourne were arrested on suspicion of assisting an offender. All three have been released on bail until 21 April.

Stan Hollis was awarded the medal for his actions during the storming of the Normandy beaches on 6 June 1944.
A campaign to have a permanent memorial to him created in his home town saw a bar dedicated to him in February.
Middlesbrough Council has now granted planning permission for a bronze statue near the cenotaph on Linthorpe Road.
The statue, which will be almost 7ft (2.2m) high and cost about ??150,000, is to be funded by donations to The Stanley E. Hollis VC Memorial Fund.
Brian Bage, the fund's chairman, said it was "good news" as it had "taken us two years to get this far".
He said the fund needed a final ??30,000 to complete the bronze figure.
Hollis was a 31-year-old sergeant major with the Green Howards when he took part in the assault on Gold Beach.
As his company moved inland, he captured several gun positions and rescued two colleagues, taking more than two dozen prisoners in the process.
As a result, he was the only one of almost 62,000 British troops to be awarded the Victoria Cross on the day of the World War Two landings.
Three months after D-Day, Sgt Maj Hollis was wounded in the leg and returned to England, where he was decorated by King George VI at Buckingham Palace.
He died in February 1972 and is buried in Acklam Cemetery in Middlesbrough.
National League side Dover Athletic have signed Ross Lafayette following his departure from Eastleigh.
[NEXT_CONCEPT]
A 17-year-old boy has been charged with the murder of a man found dead at his home in East Sussex.
[NEXT_CONCEPT]
A statue honouring the only man to win the Victoria Cross on D-Day will be built in Middlesbrough after receiving council approval.