
Jennifer H. answered 06/20/19
Certified HS/college science teacher with a passion for biology
First off, it is a misnomer to say that membranes are designed by lipids. More accurately, they are primarily composed of lipids, specifically phospholipids and a few cholesterol molecules. These are not the only macromolecules that make up the membrane, there are several different types of proteins (some with carbs attached) interspersed in and among the lipids of the membrane that serve various purposes. Like you said, there are hydrophobic amino acids, and membrane proteins contain them, but they are not entirely made up of them. The hydrophobic portions of the protein cause membrane proteins to anchor in or attach to the hydrophobic portion of the phospholipid bilayer. This whole arrangement is called the fluid mosaic model and simply means that in a fluidic lipid bilayer there are other components, proteins, freely floating around in it.
Now to your question: this goes back to the structure of a phospholipid and thermodynamics. Phospholipids are amphipathic, which means they have both hydrophobic and hydrophilic sides. The 2 fatty acid tails are hydrophobic and the phosphate head is hydrophilic, as such, the fatty acid tails tend to be attracted to each other and the phosphate heads are attracted to water. If you drop a bunch of phospholipids into a beaker of water and look microscopically, you will see that they spontaneously arrange themselves into a bilayer (2 layers) with the fatty acid tails facing each other and the phosphate heads facing the watery environment. Simply put, it is thermodynamically favorable for these lipids to arrange themselves with water on the inside and the outside of a sphere made of phospholipids, hence the basic structure of a cell membrane. But why don't proteins and cellulose do this? While many proteins are amphipathic, their structure is more complex, so will not arrange themselves into a nice neat bilayer, and cellulose, in its particular molecular arrangement, is entirely hydrophobic, therefore would only clump into a ball in the presence of water.
In summary, phospholipids are always the same structure (though they do vary in the types of fatty acids that make up their tails), simple and amphipathic, therefore always form a protocell (see wikipedia link below) in water. Proteins are more complex in their structure, and cellulose is entirely hydrophobic, so therefore cannot do the job of a phospholipid in the formation of a lipid bilayer.
I've included a link to the wikipedia pages for the protocell and cell membrane structure, they have good images that should aid your understanding of the phospholipid and lipid bilayer structure if you need it, and the role evolution plays in the structure of the cell membrane.
Good luck!
https://en.wikipedia.org/wiki/Protocell
https://simple.wikipedia.org/wiki/Cell_membrane