Linear Mixed Effects and interpreting transformations

Hi, I'm running a hierarchical linear mixed effects model in R (subject is nested in dyad). My dependent variable is a continuous variable. When I run the model I do not meet the assumption of homogeneity. A log transformation on the dependent variable does not work. However, when I use a box cox transformation, I can meet the assumption of homogeneity if lambda.hat = -0.39. However, I have no idea how to interpret the data. Is it worthwhile to do this transformation or should I look for an alternative solution?

Thanks in advance for your help.