Most lawyers will work with you on payment plans to pay the lawyer fees and you usually do not have to pay the lawyer until you win the case in court.
However you may have to pay a small upfront lawyer fee for the lawyer to begin working on your case and then you pay the rest overtime in agreed payment plans.
When you agree to make installment payments you should have no problem as long as you continue to make those agreed upon payments on time until the lawyers fees are paid off in full.
Lawyers are not required to offer payment plans however some and most lawyers do but you might find some that do not.