Once upon a time Indians could travel visa free into many countries in LatAm, which in the early nineties created a wave of immigration there with the intent of then travelling to the US. Ask a few indian in Jackson heights how they came to the US and they will tell you amazing stories.

After the deportations from the US started (which the GoI has to pay BTW), India and the LatAm countries decided it was time to plug that hole. The same occured between the former east block countries.

I seriously doubt Luxembourg has a visa free entry system with India. Its part of the shengen agreement, and LUX has nearly no direct flights from outside the EU.

The same applies to other schengen countries. Germany interprets the shengen visa norms the strictest way possible.