In a small bowl, combine the egg yolk, dijon mustard, and garlic. Whisk to combine. About 1 tablespoon at a time, drizzle oil into the egg yolk mixture and whisk (in the same direction) until the oil is emulsified into the egg yolk. Continue very slowly drizzling the oil into the egg yolk, whisking constantly until all of the oil has been incorporated into the egg yolks and forms a very thick mayonnaise. Add lime juice and whisk to combine. Taste for seasonings and adjust according to your tastes. Cover and refrigerate.