Transit Visa in Munich (for Mexico travel) for Indian passport holder

According to the German embassy in India, Indian passport holders need an airport transit visa, unless they fall into one of the exemptions (which you unfortunately do not):

Indian nationals generally require an airport transit visa for the Schengen area. This visa allows a short stop-over at an international airport only. Neither leaving the airport’s international transit area nor overnight stays in a hotel are possible. If you need to leave the international transit area (i.e. in order to catch a connecting flight at another airport to leave the Schengen area), please apply for a regular Schengen visa.

Exemptions:
a) Indian nationals holding a valid visa or residence permit from a member state of the Schengen area or Bulgaria, Romania, Croatia, Cyprus, Liechtenstein, Ireland, UK, Canada, Japan, USA (except for holders of an US “Advanced Parole Document”)
b) Indian nationals holding a valid residence permit Andorra, Monaco or San Marino
c) Diplomatic passport holders generally do not require an airport transit visa.

The same rules appear in Timatic, the system which the airlines will use to determine if you can be boarded. In relevant part:

Visa required, except for Nationals of India holding onward tickets in transit through Cologne/Bonn (CGN), Frankfurt (FRA), Munich (MUC), Hamburg (HAM), Dusseldorf (DUS) or Berlin Tegel (TXL) AND meeting one of the following conditions:

• holding a valid visa issued by Bulgaria, Canada, Croatia, Cyprus, Ireland (Rep.), Japan, Romania, USA or United Kingdom;

That's not quite the way it works. Since you booked your trip as a single ticket from Lufthansa, your luggage will almost certainly be checked through to your final destination and you won't need to go through immigration. But you might still need an “airport transit visa”, unless you qualify for some exemption (e.g. you have a valid US visa). See Do I need a visa to transit (or layover) in the Schengen area? for more details on the rules.

The other answers have already conclusively stated that you will need to acquire an Airport Transit Visa in order to transit Germany as an Indian citizen (and passport holder) en route to Mexico and back as a short-term visitor.

However, I will point out that despite needing an ATV, you will not need to go through immigration at Munich airport. As you will be on a single Lufthansa ticket, your inbound and outbound flights will both be at terminal 2. Furthermore, you will not need to enter the Schengen area, so both gates will be in the non-Schengen part of terminal 2. While you will have to go through a security check upon arrival in Munich, you will leave the security checkpoint and be right back in the departure area for non-Schengen departures. You can either navigate your way directly towards your gate or, if you have enough time, stroll around shopping and/or dining.

According to this website you do not need a transit visa at Munich.

But according to the German embassy in the USA, Indian nationals DO need a transit visa, and I'd consider that a more authoritative source. They also list what documents you need to apply.

It's probably best to contact the German embassy in India (or one of the consulates) and ask there.