Unfortunately, attorneys need more information. An applicant may be placed in removal proceedings to determine whether a deportation order and/or relief should be granted to allow the lawful permanent resident to remain in the U.S. Such a deportation can prove life altering.
Was the domestic violence complaint dismissed? Was anyone physically injured based upon the conviction? Was a restraint or requirement for domestic abuse counseling issued by the criminal court? Did he receive probation, supervision or a suspended sentence as a result of the domestic violence type conviction? Did the State law that he was convicted under require bodily injury? There may also be other violations of immigration law that can disqualify him from naturalization that you both are totally unaware of.
These, among other questions need to be answered. If the offense took place in last three to five years, then the case may be delayed or denied, where it looks like he has a conviction for immigration purposes. Again, it is possible that this is simply an arrest and will not necessarily disqualify him as a matter of law from naturalization, even if the application is delayed and he must seek a Federal Court order to get his ceremony letter.
This is why an attorney will often insist upon an appointment or teleconference before considering whether a permanent resident should file for citizenship by naturalization, among other issues of concern.
The above information is general information and does not create an attorney-client relationship.