I've moved your discussion to the Photoshop Lightroom forum, so the experts who visit that forum regularly can answer your question. But, there shouldn't be any issues installing Lightroom on your new computer.
You say that you haven't even learned how to use it. If you really mean that the the point that you haven't done anything at all with Lightroom, just give program disk to the geek squad and let them install it on the new computer. If you have actually started using Lightroom and have done even a little work, you might want to consider this: