In very simple terms, your broadband connection is being monitored at the exchange, and the speed of the connection is 'negotiated'. The exchange will increase the speed of the connection until it starts to fail (the higher the speed, the less 'stable') and will then adjust downwards to a stable connection speed.
This monitoring happens continually. When you very first connect to broadband, in fact you will see huge leaps up and down in connection speed, as the system tries to find the correct connection speed for your line.

If lightning strikes are causing minor fluctuations in the line signal, then this might be enough to cause drop outs, and the exchange will probably see this as a failure to maintain connection at the higher speed, and 'negotiate' the speed back down to a level where it can be maintained, even when there are minor fluctuations caused by the lightning.

I'm sure an expert on the subject can give more details, but thats my basic understanding.