Lawyers asking for settlement payment for divorce

After 3 years of fighting a divorce case and rights for access to my child the lawyers on both sides helped arrange a meeting with my wife and reach terms of agreement to finalize the divorce. Now both me and my wife have agreed to the terms of divorce - like amount I need to pay to her/child, visiting rights, etc.(The terms, conditions of the divorce are quite reasonable, as much as they could be under the circumstances). However, the lawyers on both sides have got together and now asking me to pay them a significant amount (4 to 5 lakhs) (which I'll try to reduce) before they help settle the matter legally (on agreed terms) and finalize the divorce. The lawyers are senior and reputed - and I know they will definitely help with the remaining formalities once they receive the payment. I'm of course not happy that they're asking for such a high amount, but if I miss this then the court judgement is likely to be worse and costlier for me. Is there a way to avoid this cost? What would you advice under the scenario?