I am travelling from Mumbai to Lafayette via Munich-Houston by Lufthansa. Do I need to claim my checked luggage to clear customs in Munich and Houston?
I know from your other question that you're on a single booking, so...
You won't claim baggage in Munich; it's just a normal international transit. You sit in the airport for a few hours until your next plane is ready to take you to Houston.
In Houston, like everywhere else in the US, international arrivals have to carry their checked baggage through Customs. You'll clear passport control, go down the escalator to baggage claim, get your bags, and take them through Customs. Immediately past Customs are airline counters where you can re-check your baggage. Conveniently these are also next to the escalators back up, which you'll use to take the TerminalLink train to Terminal B to catch your next flight.