Chandrakanth E. answered 07/09/19
PhD in plant molecular biology and genetics with 10+ years of research
Your statement is true for all eukaryotes where smooth ER is the main source of lipid biosysnthesis. However, in some cases, mitochondria also contribute in synthesizing lipids. Also, lipid biosynthesis being a complex process, a majority of steps get doenin smooth ER, but some certain specific chemical groups are added in other cytosolic locations.
Your statement is not true for prokaryotes as they lack ER and the lipid synthesis in their case takes place in the cytosol.