Which part of an individual villus forms part of the lymphatic system and absorbs fats from the lumen of the small intestine?

I believe the answer is the lacteals.

Lacteals are structures that are in the middle of each villi; they are lymphatic capillaries that absorbs dietary fats in the villi of the small intestines. Triglycerides are emulsified by bile and hydrolyzed by the enzyme lipase, resulting in a mixture of fatty acids and monoglycerides. The lacteals merge to form larger lymphatic vessels that transport chyle to the thoracic duct where it is emptied into the blood stream at the subclavian vein.