Thanks for your feedback, Wesley.

In a Poisson regression model, Lambda is a function of the regression variables. If the values of regression variables change, Lambda will change. In technical terms, Lambda _i is the conditional mean of the distribution of the y_i variable. The mean is conditioned upon a specific X=X_i. For a given set of X_i values e.g. [Day=Thursday, High=78.1,Low=62.1,Precip=0], lambda_i (the conditional mean) will attain a certain constant value and the actual y_i (the observed values) will be Poisson distributed around this mean lambda_i. For a different X_i, e.g. [Day=Tuesday, High=100.1,Low=82.1,Precip=20], lambda_i could be a different value.

Let me know if I have answered your question/concern.

'best