The answer depends on who is paying for the lawyer.
You have a right to an attorney of your choosing in criminal cases so long as you are paying for them. The courts are very liberal as to when the change can be made. The judge will almost always grant a reasonable adjournment so that the new lawyer can bring themselves up to speed on all aspects of your case, unless your proceedings are at a critical juncture (i.e. mid-trial). The outgoing lawyer has a duty to promptly provide a copy of all materials relating to your case to the new lawyer and is to refund any unused portion of your retainer, subject to the terms of the retainer agreement you signed with them.
However, if your attorney is a public defender assigned to you by the court, you may be stuck. Because of their enormous workload, it is likely that your public defender has many cases in front of the judge assigned to your case. Consequently, you shouldn't be surprised if the judge bends over backwards to defend the honor, character and competence of your assigned public defender as I have seen it happen many times. This creates a terrible problem as your only hope to get a new lawyer is to air your list of complaints about your lawyer to the judge in open court, in front of everyone including the lawyer's colleagues. I don't care what your lawyer's level of professionalism is, it would be impossible for he or she not to take your criticisms personally and develop some feelings of animosity to you and your case. Unfortunately for you, this is the same person who is likely your only hope at finding a reasonable doubt for the jury to return a Not Guilty verdict.
So what can you do? Of course the ideal solution, if you're financially able, is to meet with a number of different lawyers until you find one you trust with your freedom and one whose defense strategy you are in agreement with. If that is not possible, I strongly recommend that you schedule time to meet with the lawyer you are contemplating replacing and air your grievances to them BEFORE airing them to the judge. Do it in a non-accusatory manner so that they are not forced to be defensive. This way even if you do ultimately decide to seek a change from the presiding judge, your lawyer will not feel ambushed and your working relationship may still be salvaged if the judge denies your request.
Best of luck to you!
Legal disclaimer: All answers are for information purposes only. Answering this question or any future questions does not form any attorney-client relationship. Be mindful, that answers are limited by the limited facts presented by the questioner and are not meant to take the place of competent legal advice by an attorney fully informed of all the facts surrounding your case. Also, be aware that nothing posted in a public forum such as this can be deemed confidential or privileged communication. For a privileged private consultation, contact me at 212-385-8600 or via my website www.reasonabledoubtny.com