First, its important to understand the word deviance.  Deviance does not only refer to criminal behavior, it also refers to any behavior outside of what is normally acceptable within a society.  For example, a tribe in Africa rubs mucas on your hands and arms as a method of greeting, and the U.S. would be offended by this gesture.  Therefore, in our societies, it is viewed that some cultures contain more deviance than others.  When looking at lower-class delinquency and cultural deviance theory, it is important to understand lower-class culture.  Lower-class cultures deviate from other cultures in that they often have differences among education, religion, race, ethnicity, social status and of course income.  You need to ask yourself, how are these cultural differences related to delinquency?  How is lower levels of education, poverty, race, etc. connected to delinquency?  I would recommend that you research Robert Merton's "Structural Strain Theory".  This will give you some ideas of relating cultural deviance to lower-class delinquency in that our society promises the "american dream" to everyone.  Society sends the message that we all the the same equal opportunity as the next person.  However, this is not true based on the different levels of education, poverty, race, ethnicity, etc.  This in turn creates a structural strain that causes lower-class delinquency because most everyone wants what others have, and they will in turn break the law to get it if they don't have the same opportunity to earn it.  I know this is lenghty, but I hope it will give you a starting point to at least offer some help in answering your question...