You can use a library called "LuaInterface"
http://luaforge.net/projects/luainterface/
Heres the LuaInterface Manual (PDF):
https://warcraftaddonstudio.svn.codeplex.com/svn/trunk/src/References/LuaInterface/src/luainterface/doc/guide.pdf
"LuaInterface is a library for integration between the Lua language and Microsoft .NET platform's Common Language Runtime (CLR). Lua scripts can use it to instantiate CLR objects, access properties, call methods, and even handle events with Lua functions."
With this library in mind, we can then take a look at a question that is very similar to yours, asked by another individual.
Lua in Visual Basic.net
You can refer to this link for a LuaInterface Tutorial:
http://penlight.luaforge.net/project-pages/penlight/packages/LuaInterface/
With this said, the previous user that asked the question similar to yours posted some code that can come in handy in understanding the process you must follow to execute LUA within a VB.NET Form. It appears to be straight forward and will more than likely be sufficient for what you wish to accomplish.
Heres the code provided by user: bubby4j in his original question.
Imports LuaInterface
Public Class Form1
Public luascripting As New Lua()
Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
luascripting.RegisterFunction("DisplayText", Me,Me.GetType().GetMethod("DisplayText"))
luascripting.DoFile("script.lua")
End Sub
End Class
I hope this helps you accomplish what you have in mind! Good luck.
Dayan D.