Does data point ordering matter in LASSO regression?

I am working with Lasso on Python with a dataset of size 85×2000. I find that the ordering of the rows influence the result of the Lasso run.

I have other parameters fixed, including random states so that each run is determined. The hyperparameter is chosen through cross validation (using LassoCV in Python). However, the results change still. Is this because of the CV, or I am doing something wrong ?