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.
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National League side Dover Athletic have signed Ross Lafayette following his departure from Eastleigh.