In a general sense, yes I think what you are wanting to do is technically possible... basically they would need to have an entry added to their nameserver (for companyA.com) that points the subdomain.companyA.com to your server IP address. Then on your dedicated server, you would set it up so that requests for subdomain.companyA.com are directed to the proper folder...
Now, it being technically possible and allowed is another issue

I don't think there would be a problem given this would be a dedicated server, but since I don't work for LP can't say for sure...
And hopefully someone with a little more expertese will correct me if I'm wrong in thinking this can be done and how it would need to be setup...