I'm not a .NET developer myself, but I found a couple resources that might help:
proj.4 is probably the best projections library around; there's a .NET wrapper that seems to be maintained quite regularly here
there's another library, called Proj.NET, but the latest build is more than two years old. It's supposed to support Lambert Conic Conformal projections.
you could implement the projection yourself - i usually use either the EPSG guidance note on coordinate conversions which uses formulae that can be easily converted to code, and contains examples that can be used to test the conversion; or Snyder's 1987 book Map projections; a working manual, but that one is a bit more mathematical.
P.S.: I don't know what CRS your Lat/Lon coordinates are in, but if they're in WGS84, you may need to do a datum conversion from WGS84 to GDA94 (depending on the accuracy required) - see What is the difference between WGS84 and GDA94?