How is that even possible?
A lawsuit in the US, say, is done based on US law and a foreign lawyer would have to basically start law school all over again to have anything meaningful to say about a case.
I really don't see how this could take off.
I don't know the Indian legal system, it may be based on UK law from the colonial times and that may make it easier for Indians to deal with UK cases but still...
The actual litigation would probably not be outsourced, but some of the litigation support could definitely be outsourced (and possibly is). Some of those would be data entry, doing statistical analysis of the input data, and perhaps screening potential clients in a class action suit.