But what the comments make clear is that most lawyers think Gmail can only refer to the free email service. But Gmail is also part of the paid Google for Work service, and it comes with different terms.
Those different terms may be important, particularly if you are in Texas, because Texas Disciplinary Rule of Professional Conduct 1.05 says attorneys cannot use “privileged information of a client for the advantage of the lawyer or of a third person, unless the client consents after consultation.” By letting Google serve ads on your client communications in exchange for “free” email, it certainly seems like you and Google are both getting an advantage your client didn’t consent to.
Even if you do not practice in Texas, you should probably pay for your email service — Gmail or not — and use your own domain as a matter of professionalism instead of letting some company serve you ads based on the contents of your attorney-client communications.
Pay for your email, whether or not you use Gmail, and you will solve the problem and look like a professional.