That is a tricky question because of all the theories that have come out of the death of one of the most incredible ( and one of my favourite ) character of the XIXth century.

The most plausible theory in my opinion is the accident. That said an accidental death does not prevent in this case the story of a suicide or a failed attempt of evasion ( with our without support from the outside ).

The official statement said he did not die asphyxiated, which would mean he drowned. However according to the autopsy there was no water in his lungs so that would dismiss death by drowning. One of the important point to take into account is that von Gudden and Ludwig II went near the lake's shore after dinner and at that time Ludwig ate and drank a lot and his physical health was not as good as before ( Ludwig young and Ludwig in 1886 the year of his death ). The water was cold ( even for June ), Ludwig had eaten too much and a congestion or a syncope following cold water immersion killed him. That is for me the cause of death, an accidental and natural one. Now what happened and why was he in the water is another question for which there are three theories I think are possible : planned evasion, sudden evasion attempt or suicide. Murder is out of the question in my opinion since there are no traces of poison, injuries and he did not drown.

Situation :

Ludwig II and von Gudden walk around/near the shore of the lake. For X reason ( we'll see below ) the King takes off his hat, some of his clothes, drops his umbrella and starts heading towards the water. His belongings were found at the shore and dry which means he did take them off with the purpose of going in the lake. Seeing the King, Doctor von Gudden tries his best to prevent him and a physical confrontation follows. Ludwig II was twenty years or so younger than von Gudden and was 1,90m tall and weighted between 90 and 100 kilograms. The old doctor could not do much against Ludwig and died strangled by the monarch's hands. There is barely any enigma for the doc's death except maybe the premeditation. I honestly don't think Ludwig planned to kill von Gudden, it happened during their fight. The doctor's body was found barely a few meters away from shore while Ludwig's was further but not far enough for him to drown ( he was too tall and big as well as being an excellent swimmer according to his reputation ) which leads us even more towards an accidental death due to a stroke, heart attack, syncope or something similar. Now the theories as to why the King suddenly walked into Starnberg Lake.

Planned evasion : Despite having been arrested and official statements telling he was mad, he still had supporters both in the government ( though they must have been too scared or happy of their situation to attempt anything against the Regent Leopold ) and with the population. Indeed though he was no longer very popular in the cities he still had plenty of loyal subjects in rural areas especially the mountains. Yes, his constructions such as Neuschwanstein increased his popularity with the rural artisans and workers because it provided a lot of work, relatively well paid. The loyalty of these men had already been proven moments before Ludwig was arrested. Leopold Hitlz who was the last surviving witness told long after the events that his father ( who was commander/chief of firefighters present at the castle ) to alert the firefighters and peasants who had come to protect the castle's gates ( when themselves were alerted by the horse driver ).

So some of these loyal men could have taken part in an attempted escape plan alongside with some soldiers. Note that one theory says that Empress Elisabeth of Austria-Hungary ( Sisi ) who was his cousin could have taken part/arranged it. She was in fact on the other side of Starnberg lake, at Feldafing. She was aware of Ludwig's situation and her presence to closer to her beloved cousin could be due to either her wanting to see him ( she was sure he was not mad but eccentric ) or wanting to free him. However I don't really believe in Sisi's involvement, the political consequences her husband would face if she did so would be terrible.

Sudden Evasion : Ludwig II had all the reasons to be extremely worried about his future. Since he was " officially " insane it was sure that the new government would keep very close eyes on him and he could likely be held captive for the rest of his life. After all his brother Otto had been imprisoned since 1875 and would be until the end of his days in 1916 despite being king for 27 years after Ludwig's death ( though it certainly was better for Bavaria that Otto never ruled but that is another story ). It's easy to see that the prospect of being held captive for years had a huge impact on Ludwig who could have tried to take advantage of being alone with von Gudden and attempt an escape.

Suicide : Pretty much for the same reasons that the attempted escape. Ludwig II had already tried to kill himself when he was arrested. Again, the idea of being a captive for years could have triggered the wish to die. Knowing the personality of the monarch, this would have turned him mad for good. Wagner was dead, all he had was taken away, no more reason to live.

So I am almost sure there are no doubts any longer that Ludwig's death was natural. As to why all this happened ? The suicide idea seem very believable. Death was something the monarch found, if not attractive, just as good as living. His morbid ideas may have won on his will to live when his future turned very, very dark.

My sources are from the following books :

Ludwig II of Bavaria by Jean des Cars - Richard Wagner and Ludwig II of Bavaria by Blandine Ollivier - Ludwig II of Bavaria by Jacques Bainville -