I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
Judges have a lot of discretion in things like whether to allow a lawyer to withdraw from the case. If you were able to appeal, you would have to be able to prove that he abused that discretion, which is a fairly high standard. Most judges will allow a lawyer to withdraw when he requests to do so, because it's not considered helpful to a litigant if his lawyer doesn't want to be there, working for him. There are too many ways a lawyer can lose a case for a client.
An appeal is time-consuming, and a judge who allowed your attorney to withdraw is not likely to agree to stay the case for several months until an appeals court can hear it. To file an appeal before the court case is over, a party needs permission from the judge, which he is not likely to give. Permission is granted when resolving an issue is likely to lead to settlement of the entire case, will simplify the issues between the litigants, or will conserve court resources. Since this issue is between you and your lawyer and not you and the other party, it's unfortunately very unlikely that you'd be granted permission to do that.
If you believe that you need a lawyer to continue with your case, it would be more helpful at this point to interview other attorneys rather than to try to get your original lawyer back on the case.
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