Confusing rule about subject-verb agreement

Consider 'Lots of cheese is good for you' vs. 'Lots of cheeses are good for you.' The 'is' and 'are' cannot be interchanged.

Evidently the plurality of 'lots of X' is determined by X, not by 'lots.' Whether this rule 'makes sense' is another question, but so long as it holds, there is no contradiction with the other rule you described as applied to your problem case.

There is food left.

Food is a mass noun that does not have a plural sense the way people does. There are no discrete individuals in the concept of food (even though individual items could be intuited, such as steaks, ears of corn, etc.).

The sense of the sentence is there is food left. Lots of serves as a modifier of food, rather than of food being a modifier of lots.