Catalyzes the 3-fold methylation of ornithine lipids. Forms ornithine lipids that are mono-, di-, and trimethylated on the delta-nitrogen of the ornithine head group. an N(2)-[(3R)-3-(2-saturated-acyloxy)acyl]-L-ornithine lipid + 3 S-adenosyl-L-methionine = an N,N,N-trimethylornithine lipid + 3 H(+) + 3 S-adenosyl-L-homocysteine Optimum pH is 8. Belongs to the methyltransferase superfamily.