"I am Lukas, a student."
Translation:Ich bin Lukas, Student.
I am German. And yes, it should be "Ich bin Lukas, ein Student."
It's not exactly wrong not to use "ein". But that is a very casual form and calls for special occasions. Like when someone says: hey, Fred, what's your profession?" you could answer:" I am Luke, student!". Still, it sounds rather impolite. Even in English. In this case we would rather say: "Ich bin Lukas. Und ich bin Student."
In a normal conversation it is definitely: "Ich bin Lukas, ein Student." As someone else said, otherwise it sounds more like a last name.