With the simplex algorithm adopted by Xu (2007), extension to the Lasso estimate is not obvious. But such an extension is straightforward when an EM algorithm is applied.

Kenneth Lange, A Gradient Algorithm Locally Equivalent to the EM Algorithm, Journal of the Royal Statistical Society. Series B (Methodological), Vol. 57, No. 2 (1995), pp. 425-437 ...

Michael Elashoff, Louise Ryan, An EM Algorithm for Estimating Equations, Journal of Computational and Graphical Statistics, Vol. 13, No. 1 (Mar., 2004), pp. 48-65 ...