Is it possible to install my existing LW account on my second laptop, as the original laptop is old and slow. What is the proceedure?

Do you mean that you want to move your LW library onto the second laptop?

To move your library, look for LW's saved folder. In LW tools > options > saving will show you the location. Find that saved folder & copy it to an external drive or disc. Then copy that folder onto your second laptop.