If you're going to deliver enough lentivirus into an HIV patient to edit all the HIV out of their T-cells, you're going to provoke a massive immune response. This is not the first time people have demonstrated the ability to excise HIV from the genome - I recall a cool system that involved evolving a novel endonuclease that recognized the HIV LTRs. Aha, here: http://www.ncbi.nlm.nih.gov/pubmed/17600219

This is 2007 - doing this again with CRISPR is, frankly, just using a flashy new toolkit. The fundamental problems with gene therapy remain and are, as usual, the major hurdle to any of this shit being effective. It's easy to edit genomes in a dish; doing it in the human body is orders of magnitude harder.