Why was the Nazi party often identified with young men of the lower middle class?
There are two major reasons for this.
First, Nazism was a violent and angry ideology. It promoted a very strong "us against them" ethos and it tended to encourage the use of violence against opponents. This is the sort of ethos that would appeal to young men, particularly those who do not have a secure place in society. Young men of the lower middle class would have likely felt insecure in Germany at that time since the economy was not strong. This would have made Nazism seem attractive.
Second, Nazism was an avowedly anti-intellectual ideology. It was a populist ideology that was very simple and easy to understand. This sort of ideology that presents the world in black and white might be easier for people with limited education to understand and support.