The authors compared the weight loss to the change in triglyceride/HDL ratio and there was a very poor correlation for both groups, meaning that it was not the weight loss that affected the decrease in triglyceride/HDL ratio. Surprisingly, in the low-fat diet group, the subjects who had the largest weight loss showed the smallest change in triglyceride/HDL ratio.
In a meta-analysis published in 2020, 14 randomized controlled trials were included, where patients with overweight or obesity and with or without type 2 diabetes were given a ketogenic diet.  Irrespective of whether the patients had diabetes or not, the ketogenic diet led to substantial weight reduction and decreased triglyceride levels, and in diabetes patients, HDL increased.
The authors conclude:
“Our study findings confirmed that ketogenic diets were more effective in improving metabolic parameters associated with glycemic, weight, and lipid controls in patients with overweight or obesity, especially those with preexisting diabetes, as compared to low-fat diets. This effect may contribute to improvements in metabolic dysfunction-related morbidity and mortality in these patient populations.”
Ketogenic Diet’s Effects on Triglycerides in Normal Weight and Normolipidemic Persons
There are many studies showing a decrease in triglycerides in overweight or obese persons placed on a keto diet. The study participants often have prediabetes, metabolic syndrome, or diabetes. In these studies, the subjects often lose weight, and it is hard to know for sure if the benefits on the metabolic markers are due to the weight loss, the ketogenic diet, or both.
In a study by Sharman et al., published in 2002, 20 normal-weight men with normal lipid values (normolipidemic) were included. Twelve men switched from their habitual diet (47% carbohydrate, 32% fat, 17% protein) to a ketogenic diet (8% carbohydrate, 61% fat, 30% protein) and eight control subjects consumed their habitual diet for 6 weeks. 
In the men following a ketogenic diet, there was a significant decrease in fasting triglycerides by 33% and a decrease in lipids in the blood after a fat-rich meal (postprandial lipemia) by 29%.