No Mayo or mayonnaise does not have lactose in it.
Mayonnaise or mayo has no dairy products in the ingredients or in the mayo nor does it contain any milk or milk products.
Mayo does contain eggs though so if you're allergic to eggs then you cannot eat Mayo but if you're just lactose intolerant then you can eat mayo as it's free of lactose.
There may be some types of mayo that contain milk or lactose but most mayo that is sold in stores does not contain any milk or lactose.
Most commercially made mayonnaise is made using a mix of spices, egg yolks, and lemon juice or vinegar.
So if you're lactose intolerant mayo is okay to eat.