Is it appropriate to accept a free lunch from the hotel in this sort of scenario?
In most cases, yes, that's appropriate. It's common for a potential vendor or partner company to pay for lunch, travel expenses and minor incidentals as part of their presales process. While these companies are indeed trying to ensure that you're well taken care of, there are limits to what they spend on this. Simply put they can ensure that you don't have to worry about anything for as long as you're with them on business. But if they were spending outrageous sums of money on you or you otherwise get the impression that it feels more like attempts at bribery than common courtesy, that would be inappropriate, unprofessional, unethical and in some countries illegal.
So yes, it's common for the host of a meeting to pay for lunch and that goes double in your case since the hotel's catering is presumably also something you'd want to evaluate. Of course keep in mind that there's a decent chance you're getting the chef's very best in these situations.
The one thing you should be wary of and which was pointed out in a comment is that some companies and some governments have very strict rules on this kind of thing. Typically you would know if that applies to you but if you're in doubt you should hunt down your employee handbook, talk to your manager or HR.
Beyond that, I'd recommend using the following rule of thumb when it comes to accepting freebies: if the idea of mentioning what you received to a colleague, manager or customer makes you uncomfortable, that's a clear sign that you should probably decline whatever is offered.