I am trying to find a web site to go to, to find out where I can find my lot # and plot# on my house,

If you're in the USA, most likely place would be your county clerk's web site. However, since plats are legal documents, many counties provide information on ordering them but do not offer them online. There are some countys with online plats I've found though, like Wakulla County Florida.

Presumably you would go to the equivalent of a county clerk in your area if you're in a country outside the USA, but I can't help you there.

Some counties have the property lot info published as long as you register with the address, etc. Have you checked with your local courthouse?