Where do the lipids and proteins constituting the cell membrane get synthesized?

The lipids and proteins that constitute the cell membrane get synthesized in the Endoplasmic reticulum (ER) of the cell. This ER is divided into two types: i) Rough ER & ii) Smooth ER.

Attached to the surface of the Rough ER are round particles called the ribosomes inside which proteins are synthesized. The lipids are synthesized inside the Smooth ER.