Can I, as an employer, simply handle the sexual harassment complaint myself without an attorney?
Listen to an attorney who is focusing on your case. While often the most effective response to a complaint filed with the EEOC is that the employer took prompt action (including disciplinary measures) to remedy the situation, in some cases other approaches may be appropriate. That is expertise an attorney brings to the table.
If you claim that the matter was handled, you can expect the EEOC will investigate to determine whether your action was prompt, appropriate and effective. If the EEOC determines that the harassment has been eliminated, the victims were made whole, and preventive measures instituted, the EEOC normally will administratively close the matter. However, if your conduct is deemed legally insufficient, you may end up paying a lot of money that could have been saved if you involved an attorney early on.