Following up on lassopack, Chris Hansen, Mark Schaffer and myself have developed a package for logistic lasso regression which can be used for prediction/classification tasks with binary outcomes. The package lassologit is not yet on SSC, but you can install it from our website:

Code:
net install lassologit, from("https://raw.githubusercontent.com/statalasso/lassologit/master/lassologit_v01/")
A demonstration of how lassologit works can be found in the help file ("help lassologit") and you can also find futher information on our website: https://statalasso.github.io/

Feedback and comments are much appreciated.