Add the soy milk to a food processor and process for about 1 minute until the milk becomes foamy.
Add the vegetable oil, lemon juice, red wine vinegar, Dijon mustard, sugar and salt to the soy milk in the processor and process for about 2-3 minutes until it becomes thick and creamy.
If you feel like the mayonnaise is a little too thin, you can add a little bit more oil to it.
Notes
You can keep this cool in the fridge for about 1 week.