1) I recommend to stop using DSS API. Please switch to PARDISO API unless you're using the feature of computing the determinant.
2) There are no functions at the moment for PARDISO API which can return LU factors and permutations. We had requests for it but so far the priorities were different. You can submit a feature request to strengthen request for this feature.
3) We have the functions you want for the cluster sparse solver (which does the same operation at high-level as PARDISO but uses MPI/OpenMP parallelism [and you can run it on a single MPI]). Pease refer to the documentation for the cluster_sparse_solver_export() https://software.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-c/top/... and an knowledge base article https://software.intel.com/content/www/us/en/develop/articles/export-functionality-in-the-cluster-sp....
Let us know if you have further questions.
here is the link to the forum thread where the similar LU related questions has been discussed recently:
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