LASSO remaining features for different penalisation
Lambda is a tuning parameter („how much regularisation“, I think called alpha in sklearn) and you would choose lambda so that you optimise fit (e.g. by MSE). You can do this by running cross validation. 

This page (for the GLMnet package in R) explains how to apply Lasso in a very instructive way (alpha is the elastic-net mixing parameter here, Lambda is the tuning parameter).

You may also look at „ Introduction to Statistical Learning“, Ch. 6.2, in which Lasso is discussed in a very good way.

There are also Python Labs for the book, which should give you a blueprint for how to use Lasso in Python (see Section 6.6.2).