Everton confirmed last week that Graeme Jones, Inaki Bergara, Kevin Reeves and Richard Evans had all followed Martinez from Wigan to Goodison Park.
Wigan were keen to keep hold of Lawrence with the former Trinidad & Tobago international establishing himself as a key member of the set-up at the DW Stadium.
New Wigan boss Owen Coyle was keen to include Lawrence in his plans for the side and hoped to keep him in his coaching staff.
However, Martinez has moved to lure Lawrence away from Wigan as he finalises his backroom team on Merseyside.
Lawrence is highly-rated by Martinez and he sees the former Wrexham and Swansea defender as one of the most innovative coaches around.