Sorry for having failed to clarify this better.

Once the liver's glucose (or better-glycogen) stores are depleted, the organism "flips the metabolic switch" , that is, it shifts metabolism from lipid/cholesterol synthesis and fat storage to mobilization of fat through fatty acid oxidation and the production of fatty-acid derived ketones and glucose (gluconeogenesis). That requires the fatty acid 'raw-material' for ketone production and gluconeogenesis to be transported to the liver from the periphery. The transport vehicles for all fats are the lipoproteins (LDL, HDL and a few others). So, feeding the liver some glucose will reduce its need for the fatty acid precursors which it would otherwise require for gluconeogenesis. That's what reduces the need for lipoprotein based transport. As I mentioned in the article, this lipid energy model is not yet fully understood. But the observation of LMHRs has been established in independent studies.