You were not entitled to a stay because the court didn't relieve your lawyer but instead granted the defendant's motion. I assume the Judge's decision either didn't address your lawyer's motion to be relieved or denied it as moot. More often then not a Judge will grant the motion to be relieved and allow the plaintiff time to try and find a lawyer to see if the motion can be oppossed. It is hard to guess that did not happen here without knowing what your lawyer wrote as the basis to be relieved. You may have grounds for appeal.
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You sound like a neutral observer looking it. Are you the plaintiff? You need to find replacement counsel ASAP.
You could move to reargue (not renew because there are no new facts) but we don't know whether your attorney opposed the motion on the basis that he wanted to be relieved as counsel. A cross-motion seeks alternate relief, it's not opposition. If I was your relieved attorney, I would be worried about the result.
Also keep something very important in mind: a motion to reargue does not stop the time to file a Notice of Appeal. To preserve your right to appeal, you must file the Notice of Appeal with the county clerk where the case is pending within 30 days of the service of a copy by defendant's counsel of the court's decision WITH Notice of Entry.