It is an Asus ASQ501LAT19 with an Intel Core i5 4200u processor.
That is the biggest problem, you have a dual core processor that runs at 1.6ghz, with a max turbo boost of 2.3ghz, a speed it will only run at for a very short time.
The processor was designed for basic computing tasks, web browsing, checking email etc.
It is simply not capable of managing the demands of a processor intensive program like Lightroom.
The slow Hard Drive will be contributing to the slow performance, but replacing it with a faster one won't solve all your problems.