律师费用 for Green card -- NO.  律师费用 for H1B -- Yes. 

You do not need Green card to work, but H1B is required for you to take any job.  And any JOB related legal expenses are deductible on your Schedule A as misc expense, subject to 2% floor.

I think the reasoning behind that is you incurred those expenses to generate income, if that income is taxable, then the related expense should be deductible too.