In a small bowl, combine 1 tablespoon sugar, 1 tablespoon lime juice, 1/2 teaspoon salt, and 1 teaspoon warm water. Stir until the sugar dissolves, then set aside.
Pour 150 mL garlic-infused olive oil (or regular olive oil) into a small bowl for easy access.
Crack 2 eggs, separating the yolks from the whites. Place the yolks in a deep-bottom mixing bowl.
Use a small hand-held whisk or egg beater to begin whisking the egg yolks until they are smooth.
While whisking continuously, use a teaspoon to slowly drizzle in a small amount of oil. Whisk for about 30 seconds before adding more. Be careful not to add too much oil at once.
Gradually repeat step 5 until the mixture becomes thicker and smoother. As it thickens, you can begin adding slightly larger amounts of oil each time while whisking well to maintain consistency.
Continue whisking and adding oil in this manner until all the oil is incorporated and the mayonnaise is thick and smooth.
Once the mayonnaise is ready, add the mixture of sugar, lime juice, salt, and water. Adjust the taste if needed. Whisk well until fully combined.
Vietnamese Mayonnaise is now ready. Transfer it to a sealed jar or container and store it in the fridge. The mayonnaise will last for about 1-2 weeks.