Is LASSO regression implemented in Statsmodels?

Lasso is indeed implemented in statsmodels. The documentation is given in the url below:

http://www.statsmodels.org/dev/generated/statsmodels.regression.linear_model.OLS.fit_regularized.html

To be precise, the implementation in statsmodel has both L1 and L2 regularization, with their relative weight indicated by L1_wt parameter. You should look at the formula at the bottom to make sure you are doing exactly what you want to do.

Besides the elastic net implementation, there is also a square root Lasso method implemented in statsmodels.