Should highly correlated features be omitted before applying Lasso?
Use scikit-learn package.
In your case you need find sklearn.linear_model.LogisticRegression 

and User guide

It's clear enough for understanding. You needn't special actions to win collinearity. But instead of linear method you can use non parametric algorithm like random forest sklearn.ensemble.RandomForestClassifier.

Сompare the results of the logistic regression &amp; random forest on the test data