Microalgae lipid biosynthesis is mostly unknown with the very recent exception of Chlamydomonas reinhardtii. There is some published paper from Yonghua Li (Li-Beisson).  Usually it is assumed that "microalgal" metabolism shoudl be similar to that of higher plants. It's a great over-simplifycation because the term "microalgae" involves several times more filogenetic complexity than "higher plants". Notwithstanding, this approach seems to work. For example, lipid gene families seem to be conserved, as exemplified by DGAT genes (the two most relevant families in plants have been founded in microalgae). DGAT1 and DGAT2 have been founded in C. reinhardtii, Phaeodactylum tricornutum, Nannochloropsis, etc. Surprisingly, there is an oustanding gene redundancy for DGAT2.