As with any other new space ("sunrise industry"), LPO in India is facing some trained talent crunch. Similar to what happened in the Information Technology (IT) sector in India in the 1990s, LPO is seeing some entrepreneurs trying to fill in the training gap. www.glptest.com is one, though it isn't possible to comment just yet on the training efficacy and/or effect on employability upon receiving their certification.
Similar to what happened in IT, there is an increasing mention of the need for Industry-Academia participation in preparing a workforce to propel the nascent LPO industry into the next phase. Pangea3 and Mindcrest, two of the leading LPO companies, recently spoke about their efforts at having their staff trained by faculty from leading law schools in the US. The same piece also has comments from Indian law academicians.
Whether or not there appear NIITs and Aptechs for the LPO space remains to be seen...