Lets say that I am writing a program that supports plugins and I write one plugin that has a reference to a assembly(.net) that is licensed under LGPL, must I now make the whole project open source and under LGPL?
Consulting a lawyer is the only way to get complete, accurate advice of this nature.
That being said, you should be fine, provided you leave the LGPL code in the indepdendant, .NET assembly. If you use the code directly within your project, you may run into other issues, but as long as the .NET assembly is left as-is, and just used by your project, you shouldn't have to open up your code (although you do need to follow the other restrictions of LGPL - mainly distributing the appropriate license files, providing access to the code for the assembly, and using proper attribution).