The Reichstag fire was a fire set at the German houses of parliament on February 27th 1933. Most people would agree that Van der Lubbe did start a fire in the Reichstag, but there is much debate over whether he, alone, was to blame. This is generally due to the extent of the damage caused by the fire, and the speed at which it spread – Van der Lubbe was widely considered a mentally disturbed arsonist, he was also hungry for fame and likely to have exaggerated his responsibility for the fire, so there is some doubt that he was capable of creating such a large fire on his own. The Nazis also had stood to gain, politically, from the fire and many talked cryptically about it, as if hinting that they had a hand in it, whilst still avoiding any direct admittance.
Some historians believe that Van der Lubbe acted alone in starting the fire, and that the Nazis were simply lucky with the circumstances. Some historians also believe that Van der Lubbes reputation as a mentally disturbed half-wit was largely due to Communist propaganda used to distance themselves from Van der Lubbe and the fire.
In conclusion I think that Van der Lubbe may have started the fire alone, but this depends on whether his reputation was due to Communist propaganda or not. The Nazi party would have been very lucky for Van der Lubbe to have planned a fire on the same night as them, unless they had known of his plans and deliberately helped him out. I think either of these situations is considerable but it seems unlikely that it was all just a coincidence.