Is your office email private? No.
It is possible for your employer to read your email? Yes.
If you email your lawyer a confidential fact, could a court order your employer to divulge that email? Yes.
Your email at work is not private email. Just as your employer may go through your desk at any time, because the desk is really owned by the employer, your employer may read your email anytime, because the employer owns the email account.
It is could get worse. Your employer may be subpoenaed to turn over all your email correspondence, which would then include attorney emails between you and your lawyer. If you email your attorney from work, using the employer’s email, your email could wind up in court or in the hands of the opposing party.
Because you used a third party to communicate with your lawyer, you may have also destroyed the attorney/client privilege. For example, if you bring a friend to the office to meet with you and your attorney, the friend may be ordered to divulge what you said in your lawyer’s office Communication between client and lawyer with third parties present, destroys the privilege. Your employer’s email server is likely a third party.
If you email from your job, your boss can read your email. We tell our clients to get an email account set up just for your lawyer. Do not use your employer’s email to send out private and confidential information, meant to be seen only by you and your lawyer. It may be seen by people you do not want to see the message.