You run a potentially big risk when you use the results of a data set to choose the specific variables that you will examine in more detail from the same data. The luck of the draw will tend to make some lipid classes more or less closely associated with the 2 conditions in your data set than they might be in general. If you only focus on the classes that happen to be closely associated with the 2 conditions in this data set, your results are likely to over-state the magnitude of their true association, while you ignore what might be classes (or individual lipids within classes) that are important.
This type of problem is similar to what's been dealt with for a long time in gene-expression studies. In your case, it's best to model all the lipids together as a function of condition, use tools that can evaluate which are most closely associated with the difference in conditions (while taking into account error estimates and correcting for multiple comparisons), and then see which classes of lipids might be over-represented among the lipids that differ between conditions.
Although I haven't used it myself, there is a lipidr
Bioconductor package that seems to do all of this for you, including a "Lipid Set Enrichment Analysis" similar to what's done for gene-set enrichment. It draws on many of the tools developed originally for gene-expression work, adapting them to the particular requirements of lipidomics.
Restricting analysis to lipid classes
You could take advantage of pre-assigned lipid classes if you use some caution. If your lipid classes are based on their biochemical characteristics and not on what you find in your data, there's nothing to stop you from adding up the concentrations of all members of each class for analysis. You can then evaluate which lipid classes might differ between experimental conditions. The danger is then putting too much significance on the individual lipids within that class that this particular data set found to be different. That's where you can get into trouble: using the results from the data set to decide what statistical tests to do on the data.
You even could use the results of this study on individual lipids as preliminary data to identify particular individual lipids to evaluate in subsequent study. The practical and statistical significance of those individual lipids would then be based on the subsequent studies, not this one. The risk is that you get false positives from this initial study and waste a lot of time, effort, and expense in following up on a false positive.