Lufthansa denied boarding after coming from another delayed Lufthansa flight for 5 minutes

Lufthansa is free to close the doors and complete boarding at the time they had scheduled. If they were to wait for all the late passengers, then that flight would also be delayed and this would cause extra issues for more passengers than the few that missed it.

The other aspect is the slot for a plane to take off. If the plane is missing the allocated slot, the next one might be 1 or 2 hours later in busy airports. So they don't want to miss it.

I fully understand your frustration. I had this situation a number of times and in this situation, we all tend to see our own issue rather than the full picture. This is a natural reaction.

The good thing is that they have found a slot for you in another plane later. Sometime, some companies will leave it to you to find a solution and complain later, even if they are by law forced to find a solution for you (and not the opposite).

For the missing food, I am not 100% sure of the law. I guess it is more a service requirement than a law. Basically, passengers have bought a ticket including some catering so Lufthansa makes sure to have enough sandwiches for everybody to not piss the last passengers that wouldn't get one. It is a good service practice but it shouldn't justify 1 hour delay... In that case, no more than few minutes should be ok.

Also, on a side note, sometime, airline companies use fake reasons to justify a delay. I am not saying this is the case here but I saw that a couple of time with other airlines. For instance, I have seen a company saying that they didn't had enough crew to service the plane and so they bumped passengers to the next plane. This is a common practice for some airlines to fill one plane rather than having two 50% full planes.

The problem is, you weren't unlawfully denied boarding according to the language of the EU Denied Boarding Regulation:

1. This Regulation shall apply:

(a) to passengers departing from an airport located in the territory of a Member State to which the Treaty applies;

(b) to passengers departing from an airport located in a third country to an airport situated in the territory of a Member State to which the Treaty applies, unless they received benefits or compensation and were given assistance in that third country, if the operating air carrier of the flight concerned is a Community carrier.

2. Paragraph 1 shall apply on the condition that passengers:

(a) have a confirmed reservation on the flight concerned and, except in the case of cancellation referred to in Article 5, present themselves for check-in,

• as stipulated and at the time indicated in advance and in writing (including by electronic means) by the air carrier, the tour operator or an authorised travel agent,

http://eur-lex.europa.eu/legal-content/en/ALL/?uri=CELEX:32004R0261

(emphasis mine)

You arrived five minutes late, and boarding had already closed. There is a variety of reasons why an airline wouldn't let you board after boarding has closed, most of it operational in basis (weights and balances etc). They are completely within their rights to do this.

Is there any safety net for passengers in such situations?

Yes, you are rebooked on the next flight. Airlines are fined for late departures and arrivals, so they won't hold aircraft for connecting flights because then they may have to end up compensating entire aircraft loads of passengers rather than one or two.

Does Lufthansa (or any airline) have the right to deny boarding when they know we are on a delayed flight, and without even announcing on the speakers?

Yes. But again, you weren't denied boarding under the definition as given in the EU regulation, you missed the flight. There is no requirement for an airline to delay a flight for connecting passengers, and there is no special exemption to the fines they receive for delays caused by waiting for connecting passengers, so they simply don't do it.

After 4 hours we get into the plane. The time was passing and the airplane was not moving. Suddenly, the pilot speaking. I quote: "We are sorry for the delay, we have two extra passenger and we wait the catering company to bring us two extra sandwiches".

Catering for all passengers is a requirement for departure, the aircraft cannot depart with a short catering inventory, which is why you waited the second time around - the airline would potentially have received a fine for that, but that was unavoidable in that circumstance. They can't send catering on the next flight, while they can send passengers on the next flight...

The air space around Frankfurt is also notoriously a crowded region. The first flight probably needed to start in the time allocated.

Flight corridors are not like highways, when you hit the road when you want. There's a time-frame when you are allowed to flight. Otherwise the route will be put at disposition to other aircraft by the air traffic control.

The first flight could also have had the air bridge already removed, or it was being removed.

Useful tip for the future: If it seems like your current flight might arrive late and make your onward connection difficult, let the crew know. I have known some airlines to radio ahead, and to prioritise disembarkation for passengers with a tight connection.