Given the stricture of social mores and class in the 1910's, and that Princip murdered a royal ascendant, how was his sentence so- seemingly- lenient? 20 years in prison, even if it was a neglectful and inhumane imprisonment?
Of the assassins, two received sentences lighter than the maximum - they were the youngest, and hadn't thrown their grenades during the assassination. The other 8 received the maximum sentences. In the case of the assassins under 20 years old, the maximum sentence was 20 years with hard labour.
Thus, Princip's "lenient" sentence was the maximum allowed by law. Perhaps some - included the judges involved in the trial - felt that a more severe sentence would have been better, but Princip was tried according to the law, rather than being arbitrarily murdered. During the trial, there was discussion about Princip's age, to determine whether he was, in fact, under 20, suggesting that his sentence would have been different had he been 20. Also note that the assassins were charged with high treason, which carried higher maximum sentences than murder. The court appears to have done everything possible and legal to maximise Princip's sentence - there was no leniency involved.
Of the 11 assassins, 10 were tried in Sarajevo in October 1914 (one of the assassins had escaped to Montenegro). 16 others who were involved were also charged. Twenty-two (including all 10 of the assassins on trial) were charged with high treason and first-degree murder, and the other 3 with conspiracy charges.
All of the 10 assassins were found guilty (9 of the others were acquitted), and 8 of them received the maximum sentences possible. Gavrilo Princip (the shooter), Nedjelko Čabrinović (the bomb-thrower), and Trifun Grabež were only 19, and under the legal age of 20 required for a death sentence, were given the maximum possible sentence: twenty years with hard labour. (All three had tuberculosis, which might have influenced their decision to risk involvement in the assassination, and died of tuberculosis in prison during the war.) Vaso Čubrilović was only 17, and Cvjetko Popović 18, and received lighter sentences: 16 and 13 years respectively. The other five, all 20 and older, were sentenced to death - three were executed, and the other two had their sentences commuted to 20 years and life.
The other defendants who were found guilty received sentences varying from 3 years to life.
For more on the assassination, including background, see Christopher Clark, The Sleepwalkers: How Europe Went to War in 1914, Penguin, 2012