Is there any downside to having a ldl level as low as 37m/l?

Low energy: If you lower your LDL level below 50, it means your total cholesterol is also very low. You may have dramatically lowered your heart attack and stroke risk , but too low cholesterol can lead to decreased production if your sex hormones, such as testosterone, estrogen and progesterone. Testosterone is responsible for strength and well-being in men (and women).

Depends on cause: Patients with genetically determined low cholesterol levels (inherited) seem to do just fine , assuming all else is ok. They have no neurologic problems, no issues with fertility & no increased risk of cancer. If the low LDL is from a secondary cause, such as a gastrointestinal disorder, or perhaps due to another wasting illness, infection, etc. Than the underlying cause needs to be treated.