This paper might be of interest: "In our study we confirmed the existence of a misconception with respect to Pearson's correlation coefficient, which has not been systematically and empirically documented until now. A large number of students appears to think that, given three quantitative random variables X, Y, and Z, a positive correlation between X and Y, and a positive correlation between Y and Z, X and Z are always positively correlated."
However, if you really do have the data (and L1 to L4 are variables in the columns of a JMP table), you can just use 'Analayze > Multivariate Methods > Multivariate' to investigate. But, then again, perhaps I misunderstand your question.