Place the salmon, breadcrumbs, egg white, shallot and basil into a food processor and pulse until combined, but not puréed, then season with salt and freshly ground black pepper.
Divide the mixture into four portions and shape each portion into a burger shape. Place onto a plate and transfer to the fridge to chill for 30 minutes.
Heat the oil in a large frying pan, then add the burgers and fry for three minutes on each side, or until golden-brown all over and completely cooked through.
For the basil and lime mayonnaise, place the mayonnaise, basil, lime zest and juice, and garlic into a bowl. Mix together well and season, to taste, with salt and freshly ground black pepper.
To serve, place the lettuce and tomato slices onto one side of each focaccia bun, top with a burger and a dollop of lime mayonnaise, then add the lids to the buns. Serve on plates with a portion of chips alongside.