Objective function for Lasso (penalty on standardized scale)

Hi, I'm trying to compute the objective function after lasso fit. I see that the 'Standardize' parameter is set to be true by default, and on the matlab website https://www.mathworks.com/help/stats/lasso.html#d119e451928 it said this means that “regularization is applied to the coefficients on the standardized scale”. Then I get confused about how to compute the objective function, especially the penalty term. Any help is appreciated!

Best, Yo