This study shows that the objective function of a Lasso Poisson regression with categorical explanatory variables can be explicitly minimized in one direction. The coordinate descent method is used to obtain the optimal coefficients. Because estimates of the coefficients for each category of a categorical variable and the interpretation of these estimates depend on the baseline, it is crucial to identify the baseline category, which in the Lasso regression is the one whose coefficient is estimated to be zero. Theoretical clarifications and numerical experiments show that the baseline corresponds to a category with a coefficient equal to the weighted median of the coefficients of the categorical variable.