"He said Immigration and Customs Enforcement lawyers are abusing their power by continuing deportation efforts rather than allowing him to resume his life with his family."

Is he here illegally?  Yes?  So he's breaking the law?  Yes?  So how are they abusing their power by trying to uphold the law?

"Though born in Havana, Lima-Marin, now 39, came to the U.S. with his family when he was about 2 years old in the Mariel boatlift that ferried about 125,000 refugees to Florida in 1980. Since then, he has been a lawful permanent resident."

So though he is here illegally, he's a lawful permanent resident?  Can he produce his immigration documents that show he is here legally?  If so he should be out in no time.