If it uses .NET, then it's a DLL only by file extension, but internally it's a .NET assembly containing .NET CIL and requires a .NET runtime.
I don't think there's any easy way to use it as is on a Linux system.
A .NET compatible runtime named Mono exists for linux systems, but I haven't tried it out. You may want to look at that first.
An option to explore is source code conversion tools - C# to PHP, or C# to C++ to PHP. But I suspect, it won't be simple if you're using .NET class libraries.
Is the interface to that class library very verbose, or is it minimal and simple?
If it's minimal, then the least effort way to use it is to introduce a web service adaptor for that simple interface, deploy it in a windows machine (can be a virtual machine on that same linux system if you're using a single linux system)
and talk to it as a regular http web service via query params and receive XML or JSON or some textual representation that PHP can parse easily. There may be a performance penalty though, due to all that network traffic.
If it's a verbose interface, then tough luck - because writing a web service adaptor for it may become as cumbersome as rewriting all that logic in PHP.