This is a somewhat odd question.
I want to provide a scripting language for modding games that I build for XNA. If I was deplying these games for the PC then I would
I know this is an old question but I had similar requirements earlier and I found out about Managed Scripting. Looks like it is developed initially to solve the problem of scripting in XNA games so this is even better.
From the website:
Managed Scripting Engine
Managed Scripting provides a quick and easy solution for developers needing to implement a scripting engine into their solutions. Managed Scripting comes with a straight forward script engine that can compile & instance scripts on the fly, generating the assemblies in memory or locally on the hard-drive, and allow for dynamically invoking methods and accessing properties during runtime. ManagedScripting runs on Windows Vista, XP, Linux, XBox 360 and Microsofts Zune Player with scripts wrote using either Visual Basic or C# as the language with plans to add support for Ruby, Python and JScript.
I have not looked into it deeper myself but it sounds like what we want.
I would like to point to this related SO question, adding Javascript as an option. To some, Javascript will be more familiar than Lua.
You might want to look into VSTA, it provides C# or VB.Net. I don't know about the runtime compiling.
Lua is often used for game scripting. World of Warcraft for example offers it for all its mod makers.
Also take a look at these sites: