Rooks close on playoff slots
Gary Thorne conceded a bizarre own goal and Andy Drury made it 2-0 before half-time.
Paul Booth got the third and Jamie Cade the fourth.
Lewes have a home league game against Dorchester on Wednesday (kick-off 7.45pm) and are also at home to Oxford United in the FA Trophy on Saturday (2pm).
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Hide AdRingmer beat Eastbourne United 2-1 in the County League division one and Crowborough drew 1-1 at Shoreham.
Seaford lost 3-2 at home to Sidlesham in the Division Two Cup, while Wealden were beaten 3-1 at Midhurst & Easebourne in the league and Peacehaven went down 5-1 at home to Crawley Down. Saltdean took a point in a 2-2 draw at Steyning.