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Refer to the picture above. First, I apologize before hand if you understand this, but form the OP I suspect you may struggle with the theory. The exact nature of your problem requires more information, so I will try to help you to help yourself. I have always had success with simplicity. So, please don't read this if you remember all that theory stuff, or if you do, realize I am not trying to truly explain the intricacy of electricity, merely providing a tool to make day to day troubleshooting quicker.
Pretend you are one single electron and the diagram is a maze or game board. Your object is to get from L1 back to L, or form L2 back to L2. Regretfully the diagram does not show the transformer coils, so you must imagine that you connect from either N, or L2 back to L1, but the easiest path (path of least resistance) is through N.
So, if you have a circuit going out that contains L1, L2 and a shared N, the electron will travel from L1 through switches, loads and back along the shared N to L1. Same for the electron along L2. If the circuit feeds only receptacles and nothing is pluged in, the electron only goes to the hot side of the recep and waits for something to be plugged in.
Now break the neutral beyond all receptacles. If you plug something in to one recept or more on circuit L1, but nothing is plugged in to L2, pretend you are an electron. You run along L1 wire to the recep. you run through the cord to the load (lets say light), then back along the cord neutral, through the recep and along the neutral wire to the break and you stop. You can't go anywhere so the light does not light. You wait and wait. Along comes a person who plugs another light in, but this time to a recep on Circuit L2. Your electron runs back along the neutral to the new L2 receptacle, backwards through the light, along L2 and great, now both lights are lit. The thing is you are now going from L1 to L2, not to neutral so you are pushing 240 volts across both lights.
A couple of things to observe. This will only occur on the lights that are past the broken neutral. All loads before the neutral, your electron still gets to use the neutral highway and they will be fine. If you have a light in L2 receptacle, and check power at an L1 receptacle with nothing plugged in you will read 240 volts. If you have a light plugged in to each, but they do not use exactly the same amount of electricity, then you will read different voltages across each, but they will add up to 240 volts.
As silly as "one little electron running along the wire" sounds, I have taught several apprentices this technique with success. The silliness actually helps. I appreciate any constructive criticism.
