Proteins are considered polymers because they are made up of monomers, and lipids are not considered polymers because they are not made up of monomers. In order for the basic unit that makes up the lipid or protein to be called a monomer, the unit must occur in repetitive chains, which lipids do not.
Carbohydrates, lipids, proteins and nucleic acids are all considered macromolecules, which are giant molecules produced by the bonding of smaller molecules. Of these, macromolecules, carbohydrates, proteins and nucleic acids are considered polymers while lipids are not. The fundamental reason behind this, according to About, is that polymers are made up of monomers, which lipids do not contain. Protein monomers are amino acids and they bond together in repetitive chains just as carbohydrate monomers are sugars or monosaccharides. On the other hand, the basic units of lips are fatty acids and glycerol molecules that do not form repetitive chains. Instead, they form triglycerides from three fatty acids and one glycerol molecule.
To back this up, the University of New Mexico points out that the bonds that connect monomers dissolve in water. While this is the case in both proteins and carbohydrates, it is not the case for lipids which are not water soluble.