If you get another lawyer and the arrangement is still for 40%, the contingent fee is divided between the incoming and the outgoing lawyer at the end of the day. The court takes into consideration how much was offered to the outgoing lawyer, and how much the case actually settled for. If the outgoing lawyer got an offer of $100,000, and new lawyer upped the amount to $400,000, the outgoing lawyer would probably get a fee of $40,000 and the incoming lawyer would get the rest of the fee. This formula is not set in stone, and there may be law unique to your state that I don't know about, but this is how it generally works. Whe you hire a new lawyer (and I hope you do) your new lawyer will explain the process to you as it affects your case and work these arrangements out with the old lawyer for you
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A complete answer to your question would require also knowing why the first attorney was fired. She may have done something that affects the analysis of what she is entitled to, in anything. And, I'll respectfully suggest that in many cases it could be more complicated than what the other response suggests. For example, your first lawyer may have worked the case up until the eve of trial and then was dismissed by you after a $100,000 offer came in. If the new attorney negotiated a better deal, say $400,000, largely off the strength of the case the first attorney put together, then the split may not necessarily end up being proportional.
However: Many states have programs for settling fee disputes. The split between the two lawyers probably can't be determined until the case gets resolved and then you can all look back at the efforts and the results.