What is the lipid membrane of SARS-CoV-2 made of?
I don't know if this questions has been studied in detail even for SARS, let alone SARS-CoV-2. As noted in a comment by reuns, the virus lipid envelope is most likely derived from that of the endoplasmic reticulum. 

What we know however from from some studies on influenza viruses, that's hardly the end of the story though:


  Using rigorous virus purification, marked differences between virions and host were observed. Over 125 phospholipid species have been quantitated for three strains of influenza (HKx31- H3N2, PR8- H1N1, and VN1203- H5N1) grown in eggs. The glycerophospholipid composition of purified virions differs from that of the host or that of typical mammalian cells. Phosphatidylcholine is the major component in most mammalian cell membranes, while in purified virions phosphatidylethanolamine dominates. Due to its effects on membrane curvature, it is likely that the variations in its content are important to viral processing during infection. 


And this part is a bit of a "reverse answer", but lipid rafts on the membrane of the target cells are thought to be important for the entry of coronaviruses, including SARS. One experiment found that depleting cholesterol from the cell membranes dramatically slowed SARS virus' ability to enter them.

(Regarding how SARS-CoV-2 might come out [with different envelopes] from different cells: we only had confirmation very recently that it substantially infects intestinal enterocytes. So expecting a lot of extra details on that is a bit premature right now.)