If you bought the ticket directly from Lufthansa or some reputable website they will get you there. If you miss your connection, they will re-book you to the next available flight and may put you in a hotel overnight. If you have booked your ticket on some no-name website, this may be a problem.
45 minutes is awfully tight for a connection. Flights from DRS to MUC typically park out on the tarmac and you need to ride the bus to the terminal, which can be really slow. Make sure you notify the flight attendant that you have a tight connection so they can make sure you are getting on the first bus. More often than not there are two buses and the second bus needs to wait for the very last person to get off the plane no matter how slow they are and what item they forgot to take along.
LH typically flies an Airbus A330 from MUC to DEL. That's not a huge plane (200 people or so), so it boards pretty fast. Still boarding time will start even before you touch down, so this is a dicey proposition.
Your best bet is to call Lufthansa directly with your detailed information (ticket number, point of purchase, etc.) and ask them about your concerns. If they say it's cool, it's cool. If not, at least you don't get stranded at an airport.