It would be better to perform a COX regression with an L1 regularisation term, which would give the same type of variable selection you get from the LASSO. ISTR there has been at least one paper on this in the journal "Bioinformatics".

It would be better to perform a COX regression with an L1 regularisation term, which would give the same type of variable selection you get from the standard least-squares LASSO approach. ISTR there has been at least one paper on this in the journal "Bioinformatics". There is a good paper by Robert Tibshirani, and @miura says that this is implemented in glmnet.