While performing a multivariate analysis to know are there any significant differences among means, which test should be performed? Can LSD be applied to compute significant differences?
I am not sure if your question is still current. Hotelling T^2 is a multivariate Analog of the two sample t-test.
One possibility might be to perform your pairwise comparisons using Hotelling T^2. Just watch out for family-wise type I error (you might want to consider some sort of adjustment...Boneforrini corrections are commonly commonly used in such a setting)