HPLC grade solvents are absolutely essential if you are resuspending lipid extracts for a high-end technique such as mass spectrometry. They are less essential for the lipid extraction itself but the lower grade reagents can add more contaminants to your lipid extracts that can be visible with the high-end analytical techniques.
It is not necessarily important to use HPLC grade solvent for only lipid or fat extraction. First you decide what compound you want to analyse. If you are going to analyse entire lipid profiles using method in GC/HPLC/LC then use HPLC grade solvent since sometimes impurities in the extracted samples may interfere detector response.