LPL is largely expressed on tissues that metabolize or store a lot of fat, including muscle and adipose tissue, and it's regulated by a number of factors (1). This includes diet, hormones and other protein regulators. The current literature on LPL has shown that regulation of LPL is tissue-specific. The activity of LPL, like other proteins, may be controlled at the transcriptional or the post-transcriptional level. A review by Goldberg et al (2009) notes that the activity of LPL in adipose tissue during fasting is low, but high in skeletal and cardiac muscle. They also note that insulin increases transcription of LPL in adipose. So why the down-regulation? One of the proposed mechanisms for LPL down-regulation in adipose tissue is rapid inactivation by a protein inhibitor known as ANGPTL-4 (2)
ANGPTL-4 (also known as a fasting-induced adipose factor), is up-regulated in adipose tissue two to four-fold in response to glucocorticoid stimulation (3). It's commonly known that you have a cortisol spike within a few hours of fasting, which is intended to try and increase glucose availability, for example.
The idea is that ANGPTL-4 attempts to control the distribution of fatty acids (4). In a mouse study, Cushing et al. demonstrated that ANGPTL-4 in fact diverts uptake of fatty acids and triglycerides away from adipose tissues (5). And this study was published in August 2017, so the phenomenon is still under investigation. It makes sense though, right? Why does the adipose tissue need to continue to receive fats during fasting? They can be better served elsewhere like muscle, the brain or the liver. Not only so, but Catoire et al. also demonstrated in 2014 how the interplay between ANGPTL-4 and LPL between non-exercising and active skeletal muscle during exercise allows for fine-tuning of fatty acid delivery to sites that need it most (6). So the regulation extends to both inter- and intra-tissue needs.
In closing, LPL is regulated during fasting in a targeted manner, but it is not generally down-regulated. Regulation is controlled in a manner that allows the demands of tissues to be reactive to their environment.