"Lots of milk and sugar" or "lots of milk and (lots) of sugar"

"Lots of milk and sugar" is a parallel construction: it means "lots of milk and lots of sugar". Because "lots of" occurs twice, the parallel-construction form lets you leave it out, and it is understood that the single "lots of" is implicitly applied to every item in the list that follows it.

If the speaker wanted lots of milk and only a little sugar, they would normally say something like "lots of milk, and some sugar."

To me this seems unequivocally to mean large quantities of both milk and sugar. And that would put an end on it, except for the fact that where there is room for misinterpretation, people will misinterpret — at least part of the time.

For example, take this exchange from the classic film Pulp Fiction between Jimmie (Quentin Tarantino) and Winston Wolf (Harvey Keitel), known as "The Wolf", when the latter asks for some coffee:

Jimmie: How do you take your coffee?
The Wolf: Lotsa milk. Lotsa sugar.

Keitel's character in the film is a "fixer" and is very precise about his requirements. So Tarantino, who has in my opinion one of the best ears in Hollywood for projecting character through nuance of dialogue, probably intended this to show Winston Wolf's fussiness and exacting standards. In short, he's used to people screwing up when his directions aren't crystal clear, so he has learned to be very precise in his instruction.

I know this isn't a scholarly citation, but movies are based on life, and good dialogue reflects how different kinds of people express themselves. This exchange, I believe, is an artifact that reflects your own doubt about the coupling of "milk and sugar" in a coffee order. So although possibly 99% of the time "lots of milk and sugar" will get you a lot of each, enough doubt remains that the order will fail at least part of the time.