As with many questions like these, there is no 'one size fits all' answer. But it is worth taking the time to think about based on each lawyer's individual circumstances.
Know Your Audience
Some lawyers (and clients) think that lawyers shouldn't post too much on Facebook during business hours because those hours should be devoted to client work, and posting during business hours (especially frequent posting during those hours) may signal that the lawyer or firm doesn't have much client work to do or, alternatively, that they aren't paying appropriate attention to clients and are spending time on social media instead.
Alternatively, lawyers may not be able to post on Facebook during business hours precisely because the lawyer is working and their attention is elsewhere.
Remember that Facebook, like all social networking, is about building relationships, and for relationships to form, there must be engagement.
Any real analysis of post timing should originate with thoughts about the client (or other individuals/businesses with whom the lawyer or firm is seeking to engage). How and when does the client, potential client or referral source use Facebook? What are their expectations? When are they most likely to engage on Facebook?
What you may find is that your audience doesn't use Facebook during business hours at all - or you might find the opposite, depending upon who you want to reach and what their purpose is for using Facebook.
Experiment with posting at off hours, such as in the early morning periods , late evenings and on weekends. Then track what type of response you get and how much people engage with your posts at different times.
Scheduling Posts in Facebook
Luckily, if your audience is reading and engaging with your posts at 6 a.m. or 11 p.m., that doesn't mean you have to be physically posting at that time. There are many third party tools, such as Hoot Suite (www.hootsuite.com) or Buffer (www.bufferapp.com) which allow you to schedule posts in advance. But even then, some experts say that posting from a third party app can reduce engagement, and that posts from outside sources don't get as much play in the News Feeds of those that follow the Page.
The good news is that you can schedule posts to appear on your Timeline in the future right in Facebook.
If you are posting from your individual Facebook Profile, in order to schedule posts to appear in the future, you'll need to use the status update box on your Timeline, not the one that you see in your News Feed (see below). For some reason, Facebook doesn't provide the scheduling option from the News Feed update box.
News Feed Update Box:
The status update box you see at the top of your News Feed doesn't show the clock icon signaling that the post can be scheduled.
But if you go to your Timeline and click inside the status update box that appears there, you will see the clock icon. When you click on the icon, Facebook will prompt you to choose a year, then a month, date and time for the post.
Timeline Update Box:
Facebook Page Timeline Update Box:
Using the scheduling tool in Facebook means you don't need to be logged in to Facebook at the time you want your post to appear, and you can schedule multiple messages in advance.
Update: Thanks to some readers for pointing out that the scheduing tool on Facebook individual Timelines does not allow for posting to a future date - it only allows you to post to a past date. Hopefully, Facebook will change that. But you can post to a future date on a Facebook (business) Page using the method described above.