You can ask them some questions, including catching non family law clients, getting their contact information and forwarding their details to the relevant person at your firm.
You can get the information off of them that you need to open a new matter, and send them a follow up email indicating what the next steps are. You or a staff member will also get an email with the client's details and a link to their matter, making it easy to generate the client intake questionnaire from your phone and email it to them.
The trick is to make it different and personal. This is why automation generally takes such a long time, but what we are doing here is little bite sized automation. We just want to do this one thing, catch someone who is browsing your website and get their details. Invest an hour in getting your legal bot and landing page right, putting it into your words, your tone, and making it fit into your plan for catching clients at your website.