score:6
The Minimum Connection Time between flights landing in Terminal 2 (Lufthansa) and flights departing from Terminal 1 (Vueling) is 45 minutes. Thus technically this is a valid connection.
However valid connection does not mean that you will make your flight - it just means that the airlines will let you book such a connection when booked on the same ticket.
If you are planning to book these two flights on the same ticket, then it's potentially worth the risk. If you miss the outbound flight then it will be up to the airlines (most likely Lufthansa) to get you to your destination, either by moving you to a later Vueling flight, or more likely by putting you on one of their own flights to your destination.
However, if you are considering booking these flights on separate tickets then your chances of something going wrong are very high. One of the reasons that MUC has such a low Minimum Connection Time is that they will make arrangements for getting people directly from inbound gate to outbound gate - especially in cases of delayed inbound flights (eg, using vehicles that drive across the airport itself). If you are on multiple tickets then they will not know that you are connecting, and thus will not make any such arrangements for you.
On separate tickets it is still possible that you will make your connecting flight, but personally I would never consider such a short connection. Your odds of missing the flight are too high, and if you do miss it you'll likely have to purchase a new ticket to get yourself to your destination.
Upvote:1
On the upside, your connection would be entirely intra-Schengen so you would not need to go through immigration or anything (note that not the body EU is relevant here but the member countries of the Schengen agreement — the latter includes e.g. Switzerland and Norway while it excludes, among others, the UK and Ireland). On the downside, Lufthansa and Vueling are in two different alliances and Terminal 2 is reserved for Lufthansa and Star Alliance flights only, meaning that you would need to change terminals.
Given that Munich is a rather large airport, the distances you may have to walk only to get from your arrival gate to the central area and then onwards into terminal one and to your departure gate can be surprisingly large. If you know your way around, if your luggage is through-checked, if your incoming flight is not delayed, if there are no long queues anywhere or if you are booking this on a single ticket, I would say you can make it — and the other answer also mentions Munich airport accomodating for transferring passengers by bringing them straight to their departure gate if need be.
You mentioned in a comment to on the other answer that you already have your first ticket into Munich, so your outbound flight out of Munich would have to be a second ticket — not to mention that they are not in the same alliance and Vueling is a low-cost carrier, all of which contribute to the low likeliness of the connection being part of one ticket. On two tickets, I would not risk it, even if I didn’t have to take care of luggage (e.g. hand luggage only).