The importance of lipids for cell function and health has been widely recognized, e.g., a disorder in the lipid composition of cells has been related to atherosclerosis caused cardiovascular disease (CVD). Lipidomics analyses are characterized by large yet not a huge number of mutually correlated variables measured and their associations to outcomes are potentially of a complex nature. Differential network analysis provides a formal statistical method capable of inferential analysis to examine differences in network structures of the lipids under two biological conditions. It also guides us to identify potential relationships requiring further biological investigation. We provide a recipe to conduct permutation test on association scores resulted from partial least square regression with multiple imputed lipidomic data from the LUdwigshafen RIsk and Cardiovascular Health (LURIC) study, particularly paying attention to the left-censored missing values typical for a wide range of data sets in life sciences. Left-censored missing values are low-level concentrations that are known to exist somewhere between zero and a lower limit of quantification. To make full use of the LURIC data with the missing values, we utilize state of the art multiple imputation techniques and propose solutions to the challenges that incomplete data sets bring to differential network analysis. The customized network analysis helps us to understand the complexities of the underlying biological processes by identifying lipids and lipid classes that interact with each other, and by recognizing the most important differentially expressed lipids between two subgroups of coronary artery disease (CAD) patients, the patients that had a fatal CVD event and the ones who remained stable during two year follow-u