I am not sure if you are familiar with R, put the R package [glmnet](https://cran.r-project.org/web/packages/glmnet/glmnet.pdf) containts "extremely efficient procedures for fitting the entire lasso or elastic-netregularization path for linear regression, logistic and multinomial regression models, Poisson regression and the Cox model". 

The general syntax to "Fit a generalized linear model via penalized maximum likelihood" would be:

        fit=glmnet(x,y,family="binomial")

where x is your input matrix of independent variables, and y is your dependent variable (response variable). The binomial family would be for your binary dependent variable.