Several methods are suitable for the isolation of lipids, many of them based on the chloroform:Methanol mixtures. However, recently Matyash et al. developed a modification using MTBE what is a very good improvement to the original method. Furthermore, Sarafian et al. has also reported a very comparison of isolation methods suitable for UPLC-QTOF. These latter authors claim to have very good results using isopropanol. 

In my experience, an isolation have to as simple as possible, fast and reliable. If you need more help, please contact me. 

These above mentioned methods are very good if you are assaying total lipid analysis. However, if you are interested in fatty acid analysis you may use a direct derivatization method (Pimentel et al. 2016; Castro et al. 2014). 

Good luck and good work. 

http://www.jlr.org/content/49/5/1137.full

http://www.ncbi.nlm.nih.gov/pubmed/24820162

http://www.sciencedirect.com/science/article/pii/S2215016115000618

http://www.sciencedirect.com/science/article/pii/S0039914014004354

You can also have a look in the mat&met section of this paper.

If you just looking for lipid A, you can also try just precipitate the proteins with ethanol, evaporate to dryness and extract the pellet with nonane. You can injecta few uL nonane directly into a high flow HILIC chromatography system.